Research Collection Doctoral Thesis Mass Estimation of Transport Aircraft Wingbox Structures with a CAD/CAE-Based Multidisciplinary Process Author(s): Hürlimann, Florian Publication Date: 2010 Permanent Link: https://doi.org/10.3929/ethz-a-006361295 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection . For more information please consult the Terms of use . ETH Library
Transcript
Research Collection
Doctoral Thesis
Mass Estimation of Transport Aircraft Wingbox Structures with aCAD/CAE-Based Multidisciplinary Process
Mass Estimation of Transport Aircraft Wingbox Structures with a CAD/CAE-
Based Multidisciplinary Process
A dissertation submitted to the
ETH Zurich
for the degree of
Doctor of Sciences
presented by
Florian HürlimannDipl. Masch.-Ing. ETH
Born April 30, 1979
Citizen of Walchwil, ZG
accepted on the recommendation of
Prof. Dr. P. Ermanni, examinerProf. Dr. P. Horst, co-examiner
Dr. R. Kelm, co-examiner
2010
ISBN 978-3-909386-46-8
Acknowledgements
The present work was part of a research cooperation between the Swiss Federal Institute of Technology and Airbus Deutschland GmbH. The author would like to express his gratitude to all involved parties, in particular:
Prof. Dr. Paolo Ermanni and Dr. Gerald Kress (ETH Zurich) for giving me the opportunity to conduct research in this most formidable field of science and for the supervision of the thesis.
Dr. Roland Kelm (Airbus), whose previous research on physics-based mass estimation of aircraft structures was fundamental for this thesis, for enabling this research project and for his co-examination of the thesis.
Prof. Dr. Peter Horst (TU Braunschweig), a true expert in preliminary aircraft design, for accepting the co-examination of the thesis and also his research assistant, Mr. Johannes Rieke, for providing valuable input data for the case studies featured in this thesis.
Mr. Heinz Oltmanns (Airbus) for the financial support of this project and all involved Airbus engineers, mainly Mr. Kim Oltmann, Mr. Claus Hanske and Mr. Jörg Wenzel. Special credit is owed to Dr. Michael Dugas, whose expertise proved to be most valuable during the initial phase of this project.
The students who contributed to this thesis: Mr. Stan Banaszak, Mr. Marco Marinelli, Mr. Stefan Pfammatter and Mr. Matthias Pfister.
Lust but not least, I would like to thank my splendid colleagues and friends at the Centre of Structure Technologies – You made my day!
Abstract
Mass Estimation of Transport Aircraft Wingbox Structures
with a CAD/CAE-Based Multidisciplinary Process
Part I: CAE/CAE-based mass estimation processThe first part of the thesis describes a CAD/CAE-based multidisciplinary process for the mass estimation of transport aircraft wingbox structures. The underly-ing method is physics-based and emulates the structural design process that takes place during the preliminary design phase. A structural sizing algorithm featuring a novel FEM-based buckling criteria is used for the dimensioning of the wingbox structure. Effects of static aeroelasticity are simulated with an iterative fluid-structure coupling method. Following a recent trend in aircraft pre-design, the multidisciplinary process relies on the integrated CAD/CAE software CATIA V5 for the generation of the parametric-associative geometri-cal and structural models. Besides multi-model generation capabilities, the CAD/CAE software features custom interfaces for the generation and applica-tion of wing loads such as aerodynamic or fuel loads. Special emphasis was put on the implementation of local load introduction methods: Fuel loads, for instance, are represented by surface-distributed hydrostatic pressure loads determined by the actual fuel distribution and the acceleration vector acting on the aircraft. The finished process was used to perform a mass estimation of the wingbox of a generic long range aircraft derived from the DLR-F11 configuration.
Part II: Investigation of local load introduction methodsAccurate mass estimation of aircraft structures plays an important role during the preliminary design phase. A widespread method for mass estimation is based on the combination of computational structural analysis and a structural sizing algorithm. Based on the results of the structural analysis, the sizing algorithm adjusts the local properties of the aircraft structure (e.g. the local sheet thickness) according to a number of predefined sizing criteria. In case of
the often used fully stressed design criterion, a direct relationship between the local stress levels and local sheet thickness is assumed. As the stress distribu-tion is driven by the loads acting on the structure, it is clear that realistic load modeling and load introduction are crucial for accurate mass estimation. This publication presents a comparison of two different load introduction methods used for the mass estimation of transport aircraft wingbox structures. The first method uses low-fidelity SMT (shear, moment, torsion) loads introduced into the wingbox structure at the wing rib stations. The second method features high-fidelity nodal loads that allow for the realistic modeling of all wing load types: Aerodynamic and fuel loads are represented as surface distributed pres-sure loads, engine and landing gear loads are modeled as local loads intro-duced through dedicated load interfaces. The wingbox of a generic long range aircraft based on the DLR-F11 configuration serves as a test model for the qualitative and quantitative comparison between the two load introduction methods. The switch from SMT to nodal loads results in a small but significant increase of 4% in wingbox mass. Subsequent analyses shows that this increase is mainly caused by the use of nodal loads modeling for fuel loads, landing gear loads and engine loads. Surprisingly, the use of nodal aerodynamic loads instead of SMT loads does not have a significant impact on the structural mass of the wingbox. This suggests that aerodynamic loads, which are the predomi-nant driver for the wingbox mass, is accurately represented by SMT loads.
Part III: FEM-based buckling criterion for structural sizingStructural sizing methods are often used for the preliminary design of light-weight structures. In an iterative process, the structure is sized according to different sizing criteria based either on analytical or numerical methods. This typically includes stress, strain and buckling criteria. This publication presents a new buckling criterion for shell structures based on the Finite Element Method (FEM) buckling analysis. Compared to existing methods using analytical buck-ling criteria, the new method is not limited to specific buckling field geometries (e.g. aspect ratio, taper ratio, curvature) and buckling field boundary condi-tions. The resulting increase in buckling analysis fidelity contributes to the accuracy and the robustness of the structural sizing process.
Zusammenfassung
Massenabschätzung von Tragflügelstrukturen mit einem
Teil I: CAD/CAE-basierter Simulationsprozess zur MassenabschätzungDer erste Teil dieser Dissertation beschreibt einen CAD/CAE-basierten multi-disziplinären Simulationsprozess zur Massenabschätzung von Tragflügelstruk-turen. Der Prozess bildet einen Teil der während der Flugzeugvorauslegung durchgeführten Schritte nach und verwendet physikalisch begründete Rechen-verfahren für die Ermittlung der aerodynamischen Lasten (CFD) und für die strukturmechanische Analyse (FEM). Ein iteratives Dimensionierungsverfahren, welches die FEM-Methode miteinbezieht, wird für die Strukturauslegung des Tragflügels verwendet. Effekte der statischen Aeroelastik werden mittels eines iterativ gestaffelten Kopplungsverfahrens (Fluid-Struktur-Kopplung) abgebil-det. Aufgrund des steigenden Interesses an CAD-basierten Methoden in der Flugzeugvorauslegung, wird für die Erzeugung der parametrisch-assoziativen Geometrie- und Strukturmodelle die CAD/CAE Software CATIA V5 verwendet. Besonderes Augenmerk wurde auf die Implementierung physikalisch korrek-ter Lasteinleitungsmethoden gelegt: Treibstofflasten werden, abhängig vom Betankungs- und Flugzustand, als flächenverteilte hydrostatische Drucklasten direkt auf die Innenseite der Flügeltanks aufgebracht. Der erste Teil schliesst mit der Massenabschätzung eines auf der DLR-F11 Konfiguration basierenden Langstreckenflugzeuges.
Teil II: Untersuchungen zur Lasteinleitung von FlügellastenDie Möglichkeit zur präzisen und zuverlässigen Massenabschätzung ist von grosser Wichtigkeit während der Flugzeugvorauslegungsphase. Integraler Be-standteil der in Teil I beschriebenen Methode ist ein Verfahren zur Strukturaus-legung. Eine weitverbreitete Methode basiert auf der iterativen Kombination
der FEM-basierten Strukturanalyse und eines lokalen Dimensionierungsver-fahrens (engl. Sizer). Basierend auf den Ergebnissen der Strukturanalyse, und unter Einbezug einer Reihe von Dimensionierungskriterien, werden vom Sizer die lokalen Eigenschaften der Flügelstruktur (z.B. die Hautdicke) angepasst. Im Falle des häufig verwendeten Spannungskriteriums wird dabei ein direkter Zusammenhang zwischen den lokalen Materialspannungen und der Materi-aldicke angenommen. Da die Spannungsverteilung in der Struktur von den angreifenden Lasten mitbestimmt wird, kommt der korrekten Modellierung der Lasteinleitung grosse Bedeutung zu. Im zweiten Teil dieser Arbeit wird ein Vergleich zweier Lasteinleitungsmethoden für Flügellasten durchgeführt: Die erste Methode verwendet niedrig aufgelöste SMT-Lasten (Querkraft, Biegung, Torsion), welche über die Flügelrippen verschmiert in die Flügelstruktur einge-leitet werden. Die zweite Methode verwendet hoch aufgelöste Knotenlasten (engl. Nodal loads), welche eine realistische Abbildung aller Flügellasten er-laubt: Aerodynamische Lasten und Treibstofflasten werden als flächenverteilte Drucklasten aufgebracht, Triebwerks- und Fahrwerkslasten werden als lokale Lasten über geeignete Schnittstellen (z.B. Fahrwerksanbindung) in den Flügel-kasten eingeleitet.
Im Rahmen einer Vergleichsstudie werden beide Lasteinleitungsmethoden qua-litativ und quantitativ miteinander verglichen. Der Wechsel von SMT-Lasten zu Knotenlasten resultiert in einem kleinen, aber signifikanten Anstieg der Strukturmasse des Tragflügels von 4%. Weiterführende Analysen zeigen, dass dieser Anstieg primär durch die Verwendung von Knotenlasten für Treib-stofflasten, Fahrwerkslasten und Triebwerkslasten zu Stande kommt. Überra-schenderweise hat die Verwendung von Knotenlasten anstelle von SMT-Lasten für die Modellierung der aerodynamischen Lasten keinen signifikanten Einfluss auf das Strukturgewicht des Tragflügels. Dies lässt den Schluss zu, dass aero-dynamische Lasten, welche als einer der wichtigsten Treiber der Strukturmasse gelten, ausreichend genau durch SMT-Lasten repräsentiert werden.
Teil III: Ein FEM-basiertes Beulkriterium für die StrukturauslegungTypische Dimensionierungskriterien, wie sie von Sizern in der Flugzeugvoraus-legung verwendet werden, umfassen Spannungs-, Dehnungs- und Beulkriteri-en. Im dritten Teil der Dissertation wird ein neues, FEM-basiertes Beulkriterium für Flächentragwerke vorgestellt. Im Vergleich zu herkömmlichen, auf analyti-schen Ansätzen basierenden Beulkriterien, ist das FEM-basierte Beulkriterium
nicht auf vordefinierte Beulfeldgeometrien (z.B. in Bezug auf das Seitenver-hältnis oder die Krümmung) oder Randbedingungen (Einspannung) limitiert. Im Rahmen einer Vergleichsstudie wird die Ergebnisqualität und die Leistungs-fähigkeit des FEM-Beulkriteriums untersucht und bewertet.
Table of Contents
Introduction
1 Introduction 1
1.1 The economics of structural efficiency 1
1.2 The aircraft design and development process 2
1.3 State of the art in mass estimation 4
1.4 Identification of the research needs 15
1.5 Goals of this thesis 16
1.6 Thesis overview 17
Part I: CAD/CAE-based mass estimation process
2 Introduction to Part I 19
2.1 Multidisciplinary process for mass estimation 21
2.2 Load introduction methods 21
2.3 Structural sizing method 22
2.4 CATIA V5 (CAD/CAE) 23
2.4.1 Automation capabilities 23
2.4.2 Support for parametric associative modeling 25
During the last ten years, the global airline industry experienced an average an-nual growth rate of 7% by revenue. According to the latest IATA (International Air Transport Association) forecasts, the total revenues of the global airline industry are expected to reach 591 billion USD for 2011 [1]. Despite these im-pressive figures, the total net profit is expected to be 5.3 billion USD resulting in a net profitability (as percentage of revenues) of only 0.9%.
The diminishing net profitability is mainly attributed to two developments: Firstly, the successful market entrance of low-cost carriers leading to an in-dustry-wide erosion of airline ticket fares. Secondly, the ever-rising fuel prices which have a direct impact on operating costs and therefore profitability of the airlines. As a matter of fact, in 2006, fuel replaced labour as the largest single cost item for the airline industry [2].
As these developments are both ongoing and irreversible, pressure on the major airframers to offer fuel-efficient aircraft is going to increase even more in the future. Besides fuel efficient engines, lightweight materials and structures are the key to efficient aircraft and low operating costs. However, the aircraft industry is also under pressure to stabilize development costs and reduce the development time. According to industry sources, the total development costs for the Airbus A380 Megaliner are believed to total 15 billion USD. It comes as no surprise that the major airframers are trying to delay the mid-life updates of their highly successful but aging single aisle aircraft families - the Boeing 737 and the Airbus A320 - in an effort to conserve manpower and working capital [3].
With the CAD/CAE-based mass estimation process presented in this thesis, the author hopes to make a small contribution towards the development of design tools for the time- and cost-efficient development of future aircraft.
2
Introduction
1.2 The aircraft design and development process
1.2.1 Airbus milestones modelAircraft design and development takes place in several phases spanning the entire development cycle from the first product ideas and the identification of market opportunities right to the service entry of the finished aircraft. Fig. 1 shows the early stages of the Airbus milestones model as described by Mechler [4]. The model starts with milestone M0 (product ideas established) and ends with milestone M15 (program target reached). The stages that are relevant for this work are highlighted in gray color (M2-M5).
1.2.2 Preliminary design phaseMore simply, the design process can be divided into the preliminary and the detailed design phases. During the first phase, the conceptual design phase, engineers investigate different aircraft designs with respect to future market requirements and economic and technical viability. This phase is mainly driven by the experience and creativity of the involved engineers. After suitable air-craft designs are identified, the preliminary design phase starts. During this phase, the performance of different aircraft configurations is evaluated and benchmarked in order to find an optimal design for further development in the detailed design phase. Fig. 2 shows the cost development during the pre-liminary and detailed design phases. It is evident that design changes are most cost-efficiently implemented during the preliminary design phase when the overall design is still open for changes.
1.2.3 The importance of fast and accurate mass estimationA key indicator for the performance of an aircraft design is given by its struc-tural mass. The lower the structural mass, the lower the empty weight which in turn allows for both an increase in payload and/or range, both of which have a direct positive impact on the profitability of the operating airline. It is therefore mandatory for aircraft manufacturers to be able to perform fast and reliable mass estimation of aircraft structures during the early stages of the aircraft development process.
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1 Introduction
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Figure 1: Airbus milestones model (early stages)
Figure 2: Costs during aircraft development
4
Introduction
This is exactly where computational methods add value: Their automation capabilities allow for the evaluation and optimization of a large number of individual designs during a short time leading to a reduction of both develop-ment costs and development time [5]. An introduction to mass estimation methodology and an overview and comparison of existing tools and processes is given in the following chapter.
1.3 State of the art in mass estimation
1.3.1 Classification of mass estimation methodsThe methods used for mass estimation can be classified as either empirical or physics-based. Empirical methods rely on existing statistical data of previously analyzed or built aircraft. The structural mass of a new aircraft configuration is calculated by inter/extrapolation of existing data according to predefined geometrical, structural or operational parameters [6,7]. With physics-based methods on the other hand, the structural mass results from a multidisciplinary process that includes the structural analysis and dimensioning of aircraft struc-tures that are stressed according to select loadcases. Because physics-based methods do not rely on historical data, they are preferable to empirical meth-ods particularly with regard to the analysis of unconventional aircraft configu-rations [8] or aircraft structures featuring new material technology such as carbon fiber-reinforced plastics (CFRPs) [9-13]. Notable representatives of this category are the computational tools FAME-Wing, PrADO and most recently the MDCAD framework. Although numerous other (undisclosed) software tools are expected to exist, the aforementioned exponents are of particular interest because they are well documented by scientific publications such as journal papers, conference proceedings or PhD theses.
In addition to the purely analytical or physics-based methods, there are also mixed approaches that try to unite the advantages of each method in one tool - e.g. the speed of the analytical methods with the fidelity of the physics-based methods. An example of a hybrid approach is presented in [14]. However, in the further course of this thesis, the author concentrates on physics-based mass estimation methods only.
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1 Introduction
1.3.2 A survey of existing tools and frameworks (physics-based)In order to compare the existing tools and processes, the typical characteristics of a physics-based mass estimation process need to be defined first: Fig. 3 shows the author’s definition of a basic mass estimation process for aircraft wingbox structures: The actual process can be viewed as a «black box» with an input and an output. Mandatory inputs include the description of the air-craft configuration (both the geometry and the structure), the loadcases and the parameters used for the structural dimensioning (sizing). In its most basic form, a mass estimation process returns the structural mass of the wingbox structure as the output. In the author’s view, an autonomous physics-based mass estimation process is defined by the following six characteristics:
i) Multi-model generation capability: Automatic generation of the geometri-cal and structural models and the models used for load generation, such as aerodynamic models. In order to guarantee consistency between the
Figure 3: Characteristics of a basic mass estimation process
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Introduction
models, all models are ideally based on the geometrical model. The multi-model generation capability can be either CAD based (as described in this thesis) or non-CAD based.
ii) Load generation capability: Aircraft wings are subject to a variety of dif-ferent loads types. This mainly, but not exclusively, includes aerodynamic loads, fuel loads, inertial loads, landing gear loads and engine loads. As mentioned in paragraph 1.3.1, physics-based mass estimation methods rely on dedicated methods for the generation of load types (e.g. CFD meth-ods for the aerodynamic loads).
iii) Load application capability: This module handles the application of the loads to the structure. This functionality is crucial, as effects of local load introduction can only be replicated and analyzed with appropriate load application interfaces.
iv) Structural analysis capability: Depending on the fidelity of the structural model, the structural analysis is either based on low-fidelity beam models or high-fidelity FEM-models. The results of the structural analysis (e.g. the stress distribution within the structure) is the bases for structural sizing.
iv) Structural sizing capability: The structure is dimensioned according to pre-defined structural sizing methods and parameters. As aircraft structures are subject to different loadcases, multi-loadcase capability is mandatory for the structural sizing module.
vi) Aeroelastic feedback capability: In case of aircraft wings, the elastic de-formation observed during flight has an effect on the aerodynamic load distribution. This aeroelastic coupling is covered by a feedback functionality built into the mass estimation process.
FAME-WFAME-W (Fast and Advanced Mass Estimation Wing) is a multidisciplinary weight prediction tool developed at Airbus Germany [15]. It is able to perform mass estimation of transport aircraft wingbox structures with respect to effects of static aeroelasticity. FAME-W is part of a whole family of FAME tools that not only covers the wings but also the fuselage, the secondary structure (e.g. the Flaps) and the systems. Fig. 4 shows the actual workflow of the FAME-W design process. An in-house software code is used for the generation of the geometrical model which is shown in Fig. 5. Analytical methods are used for
7
the analysis and the dimensioning of the wingbox structure which is repre-sented by analytical beam model (Fig. 6). The fidelity of the load introduction method is comparably low as all load types are introduced as condensed loads. Besides the actual mass estimation capability, FAME-W also allows for the op-timization of the spanwise lift distribution. This means that the spanwise twist angle of the profile cross sections is automatically adjusted in order to reach a predefined lift distribution. Despite the relatively simple geometrical and struc-tural models, FAME-W has two important advantages: Firstly, it offers a high computational efficiency. This enables FAME-W to be used as an optimization tool as demonstrated in the successful optimization of the A380 lift distribu-tion in 2000 [15]. Secondly FAME-W is constantly re-validated against weight book data of existing aircraft configurations in order to assess and improve the accuracy of the results [16].
1 Introduction
Loads loop(for each individual load case)
Structure dimensioning WeightsAerodynamic design
Flight performance calculation
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- Influence of flexibility- Rudder effectiveness- Divergence problem
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- Response problem- Stability problem (flutter)
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Figure 4: FAME-W design process [15]
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Introduction
Figure 6: FAME-W structural model [17]
Figure 5: FAME-W geometrical model (wireframe) [17]
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1 Introduction
PrADOPrADO (Preliminary Aircraft Design and Optimisation Program) was originally developed by Heinze [18] at the Institute of Aircraft Design and Lightweight Structures of the TU Braunschweig. PrADO has since been subject to constant development and refinement. A comprehensive overview PrADO with a focus on the implementation physics-based methods for the load generation and structural dimensioning is given by Österheld in [19]. PrADO was recently mod-ified to cover not only conventional aircraft configurations but also blended wing body configurations [8].
Unlike FAME-W or the MDCAD framework introduced in the next section, PrADO is a modular software framework for the design and optimization of the entire transport aircraft with regard to operational and even economical aspects through the use of a dedicated cost model.
Fig. 7 shows the geometry model of an Airbus A320 generated with PrADO. The geometry model includes the fuselage, wings, HTP, VTP, landing gear, engines, pylons and winglets. As with FAME-W, the geometry generator used by PrADO is not CAD-based but instead relies on an in-house software code using NURBS [20]. According to [19], the use of CAD methods was considered but turned down in favour of an in-house code due to concerns regarding licensing, robustness and computational efficiency. Nevertheless, the model is very detailed and in case of the wings includes the outer geometry as well as the geometry of the wingbox structure and the secondary structure (flaps, slats, spoilers and ailerons).
The corresponding structural model, which is derived from the geometrical model, is shown in Fig. 8. In contrast to FAME-W, PrADO can be configured to use either an fast-running analytical or a higher fidelity but computationally more expensive FEM-based method for the structural analysis and dimension-ing of the aircraft structure. The latter method is based on an in-house devel-oped FEM tool (IFL-EFEM).
Aerodynamic loads, which are the most important loads by magnitude, are calculated with the higher-order panel code HISSS [21,22]. Effects of aeroelas-ticity can also be taken into account with PrADO. This includes effects of static as well as dynamic aeroelasticity (flutter analysis).
Together with FAME-W, PrADO marks the state of the art in physics-based mass estimation in aircraft pre-design.
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Introduction
Figure 8: PrADO structural model (Airbus A320) [8]
Figure 7: PrADO geometrical model (Airbus A320) [8]
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1 Introduction
MDCADThe MDCAD (Multi-Disciplinary Concept Assessment and Design) framework was originally developed by QinetiQ for the analysis and optimization of mili-tary and civil aircraft configurations [23]. According to [24], MDCAD is mainly used to investigate the impact of novel technologies and systems such as fuel systems [25], composites, land gears and other systems.
The workflow of the MDCAD framework is shown in Fig. 9, showing the typi-cal characteristics of a physics-based mass estimation process including model generation (both geometrical and structural), load generation, load applica-tion and structural sizing. Python-based [26] scripting is used to automate the process across a network of machines.
What differentiates MDCAD from both FAME-W and PrADO is the fact that it uses the CAD/CAE software CATIA V5 as a geometry model generator. MD-CAD incorporates automated links from CAD to FEM for the generation of the structural model and from CAD to CFD for the generation of the aerodynamic model [27]. The FEM solver MSC.Nastran is used for the structural analysis.
Figure 9: MDCAD Framework [24]
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Introduction
Although MDCAD is in many ways similar to the multidisciplinary process pre-sented in this publication, significant differences exist regarding the fidelity of the loads modeling as well as the generation of the structural and aerodynami-cal models which is performed by third-party software outside of CATIA V5.
1.3.3 Comparison of FAME-W, PrADO and MDCADFig. 10 shows a qualitative comparison of the physics-based mass estimation tools FAME-W, PrADO and MDCAD. Each of the tools has its own advantages and disadvantages: The non-CAD-based tools FAME-W and PrADO are both industry-proven and validated. FAME-W offers the highest computational effi-ciency but has deficits with regard to the fidelity of the computational models. As a consequence, the possibilities to analyze local load introduction effects
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Figure 10: Qualitative comparison of existing mass estimation tools
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1.1 Paragraph Name
are very limited. PrADO on the other hand offers high fidelity models but for the price of lower computational efficiency. The only tool that is based on CAD/CAE methods, the MDCAD framework, does neither reach the computa-tional efficiency of FAME-W nor reach the level of fidelity achieved by PrADO. This comparison clearly shows that there is room for a novel mass estimation process that is both CAD/CAE-based and offers high fidelity for all associated models (geometrical, structural, loads).
1.3.4 Other relevant research
Investigation of parametric-associative CAE methods by LedermannThe work by Ledermann is a cornerstone of this thesis [5,28,29]. In his work, Ledermann investigated the use of parametric associative CAD/CAE methods in preliminary aircraft design. This consequently led to the development and implementation of the Knowledge Pattern modelling functionality within the CAD/CAE software CATIA V5.
In a strict sense, the CAD/CAE-based process developed by Ledermann for the optimization of wingbox structures can not be classified as a physics-based mass estimation process as it lacks provisions for the generation of loads
Figure 11: Aircraft geometry model by Ledermann [29]
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Introduction
and provides only an interface for already existing SMT cut load distributions (an introduction to SMT cut loads is given in Part II of this thesis). Neverthe-less, Ledermann demonstrated that the CAD/CAE software CATIA V5 can be successfully used for the generation of (variable fidelity) geometrical and structural models during aircraft pre-design. He also performed the successful integration of CATIA V5 into an existing MDO framework using GAs (ge-netic algorithms) [29]. An example of an aircraft geometry generated with the CATIA V5-based approach is shown in Fig. 11.
Ledermann closed his thesis with a prospective outlook on CAD/CAE-based MDO. Based on an exemplary multidisciplinary optimization of a CFRP wing box [27], he compiled a list of topics that are open for further research in order to increase the accuracy, efficiency and flexibility:
i) Need for a common geometry basis: MDO requires the exchange of data between different disciplines such as structural mechanics and fluid dy-namics. A common geometry basis is the prerequisite for accurate and efficient data exchange.
ii) Integration of CFD codes: Ledermann stated that CFD tools need to be in-tegrated further into modern CAE frameworks in order to better map the highly multi-disciplinary processes of aircraft pre-design [30]. Because of its high computational efficiency, he identified the CFD code BLWF (Boundary Layer Wing Fuselage) as a promising candidate for the integration into the CAE environment of CATIA V5.
iii) Coupling libraries: Multi-disciplinary simulations involve different simula-tion codes that need to be coupled. As an example, Ledermann presents an fluid-structure coupling library developed at the Centre of Structure Technologies of the ETH Zurich [31].
iv) Load introduction: According to Ledermann, cut loads are still the state of the art in aircraft pre-design. The main reason is their ease of use which facilitates the exchange of loads between different tools and processes. However, cut loads are not suitable for the analysis of local load introduc-tion effects. In order to analyze these local effects, Ledermann proposes the introduction of generic interfaces for the integration of local loads within the CAE environment.
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1.1 Paragraph Name
1.4 Identification of the research needs
The research topics identified by Ledermann in the previous section can be aggregated as follows:
i) Increased flexibility through the use of CAD/CAE-based methods: A first trend is marked by the increased interest in commercially available CAD/CAE software solutions for the generation of geometrical and computa-tional models within multidisciplinary processes [24,28,32-34]. This offers two advantages: Firstly, the developer of the process has access to the already built-in set of CAD/CAE features offering a potential reduction in development time and costs. Secondly, it enables the straightforward ex-change of geometrical and computational models with other development partners through the use of standardized software and data formats. This is an important advantage as collaboration efforts between different part-ners or company departments are often impeded by the use of proprietary software tools and file formats [35,36].
Use of modern CAD/CAE methods
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non-CAD-based
FAME-Wing(by Airbus)
PrADO(by TU Braunschweig)
Non-existent!→ Need for research
MDCAD(by QinetiQ)
Loca
l loa
dsC
onde
nsed
load
s
CAD-based
low high
Figure 12: Research needs
16
ii) Increased fidelity through local load introduction methods: A second trend in aircraft pre-design is supported by the increased use of nodal loads in-stead of SMT (Shear Moment Torsion) cut loads for the structural analysis. Nodal loads refer to forces and moments acting directly on the discretiza-tion points (nodes) of the FEM model. Cut loads by contrary are condensed loads distributed along a virtual axis through the aircraft wing. While cut loads are well accepted and easy to handle, nodal loads offer a higher degree of fidelity and are better suited to reproduce effects of local load introduction. Because the structural sizing depends on the stress distribu-tion, which itself depends on the aircraft loads, realistic load introduction modeling is vital for the accuracy of the mass estimation process.
An analysis of the mass estimation tools described in section 1.3 with regard to both the use of modern CAD/CAE tools (increase in flexiblity) and the use of local loads (increase in fidelity) reveals the need for further research (Fig. 12).
1.5 Goals of this thesis
The present work aims to answer the following questions: Firstly, can the CAD/CAE software CATIA V5 be used as a multi-model generator and load proces-sor within a multidisciplinary wingbox mass estimation process? If so, what are the specific advantages, disadvantages and limitations of using CATIA V5 in terms of functionality and performance compared to existing solutions? Secondly, can this process be adapted towards the use in a multidisciplinary optimization framework? Thirdly, what are future fields of improvement for CATIA V5 regarding the application in multidisciplinary processes?
Upon successful completion of the multidisciplinary mass estimation process, the following questions regarding different load introduction methods shall be answered: Does load introduction based on nodal loads lead to significantly different results in wingbox mass compared to load introduction based on SMT loads? If so, what is the impact of the different load types on the individual components of the wingbox structure and what general recommendations for the load introduction modeling can be given?
17
1.1 Paragraph Name
1.6 Thesis overview
The thesis is presented in three parts: The first part introduces the CAD/CAE-based mass estimation process, the second part focuses on the investigation of different load introduction methods and the third part concludes with a novel FEM-based buckling criterion used for structural sizing. The content of each part is, with minor modifications, also available as a dedicated scientific publication [37-39].
CAD/CAE-based mass estimation process for transport aircraft wingbox structures
2 Introduction to part IThe first part of this thesis gives an in-depth review of the CAD/CAE-based multidisciplinary process for the mass estimation of transport aircraft wingbox structures. The finished process is then used for the dimensioning of the wing-box structure of a generic long-range aircraft based on the DLR-F11 configura-tion. The primary objective of this case study is to establish a suitable proof of concept for the CAD/CAE-based mass estimation process.
Outboard engine
Slats
Ailerons
Flaps
Spoilers
Ribs
Center wingbox
Front spar
Middle spar
Rear spar
False rear spar structure
Inboard engine
Figure 13: DLR-F11 wing planform
20
Part I: CAD/CAE-based mass estimation process
Mul
tidis
cipl
inar
y pr
oces
sO
utpu
t
Aer
oela
stic
loop
Sizi
ng lo
op
Postprocessing
Preprocessing
DeflectionsLoads
Geometry results (jig/flying shape)
FEM results (sized structure, mass)
CFD results (loads, coefficients)
Inpu
tAircraft parameters (geometry, structure)
Loadcase parameters
Structural sizing parameters
Structural model (CAE)
Geometry model (CAD)
Load generation
FEM analysis
Structural sizing
Figure 14: Multidisciplinary process
21
2 Tools and methods
2.1 Multidisciplinary process mass estimation
True to physics-based mass estimation, the multidisciplinary process follows the steps of model generation, load generation, load application, structural sizing and postprocessing including weight accounting (Fig. 14). Input param-eters specifying the aircraft and wingbox geometries, the material properties, the loadcases and the structural sizing criteria are provided by the user in the form of text files. The CAD/CAE software CATIA V5 serves as a multi-model generator for the geometry (CAD), structural (CAE) and aerodynamical (CFD) models. Exemplary case studies illustrating the specific use of CATIA V5 are given in chapter 3 of this publication.
The multidisciplinary process features modules for the generation and process-ing of all static loads including aerodynamic loads, fuel loads, engine loads, landing gear loads and inertial loads of both structural and non-structural masses. A CFD tool based on potential flow theory (BLWF) is used for the cal-culation of the surface-distributed aerodynamic loads. The processing of the aerodynamic loads as well as the generation and processing of the fuel loads is managed by custom MATLAB scripts. An iterative fluid-structure coupling method is used for the calculation of static aeroelastic deflection of the wing (flying shape). A trim routine for static flight maneuvers is not implemented in the current version of the mass estimation process. The engine thrust for every flight loadcase is determined by the glide ratio and the total lift force. The dimensioning of the wingbox structure is performed with an FEM-based structural sizer. The process outputs include the thickness and weight distri-bution of the wingbox structure, the geometry of the flying shape and the aerodynamic results for all loadcases involving flight loads.
2.2 Load introduction methods
The multidisciplinary process supports two load introduction concepts: SMT loads and nodal loads. With SMT (shear, moment, torque) loads, wing loads are represented as condensed loads distributed along a virtual axis running through the wing in spanwise direction. The actual load introduction into the FEM model of the wingbox is performed with the help of non-stiffening inter-polation elements (Nastran RBE3s [40]) connecting the load application points to the rib boundary curves. SMT cut loads are still the state of the art because they allow for the straightforward exchange of wing loads between different
22
Part I: CAD/CAE-based mass estimation process
computational models. Nodal loads on the other hand aim for improved ac-curacy: All wing loads are represented by individual load vectors acting directly on the nodes of the FEM model. This allows for a more accurate reproduction of load introduction effects as experienced with engine, landing gear or fuel loads. A dedicated loads interface was implemented in CATIA V5 to support the use of both SMT and nodal loads [38]. A comparison between both load introduction methods is given in Part II of this thesis.
2.3 Structural sizing method
An FEM-based structural sizing algorithm is used for the dimensioning of the wingbox structure. Structural sizing is a local optimization method: In an itera-tive process, the local properties (e.g. the sheet thickness) of the FEM elements are adjusted according to predefined sizing criteria. The range of implemented sizing criteria includes stress, strain, buckling and fatigue criteria. Special em-phasis was put on the buckling criteria: Besides a criterion based on analytical handbook methods [41], a novel buckling criterion based on FEM buckling analysis was implemented [39]. A review of this new approach to buckling optimization is given in Part III of the thesis.
Cus
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CAA
Visual Basic
Used forthis work
CATIA Knowledgeware
Native CATIA (e.g. Parameters)
Figure 15: CATIA V5 automation tiers
23
2 Tools and methods
2.4 CATIA V5 (CAD/CAE)
CATIA V5 by Dassault Systèmes is the predominant CAD/CAE software in the aerospace industry. The terms CAD and CAE originally stand for Computer Aided Design and Computer Aided Engineering. In the context of this thesis, they are used to designate the drafting and design capabilities (CAD) and the structural analysis capabilities (CAE) of this software. The seamless integration of both CAD and CAE capabilities in one software package is a key feature of CATIA V5.
2.4.1 Automation capabilitiesFour automation tiers with different degrees of customizability and usabil-ity exist in CATIA V5 (Fig. 15). The most important automation tools (CAA, VBScripts, Knowledge Patterns and UDFs) are introduced in this section. The highest degree of customizability and performance is offered by the CAA C++ API (Application Program Interface) [42]. The sparse documentation and the comparably complex program language are the main reasons why CAA is often dismissed in favor of Visual Basic (VBScripts). Although significantly less powerful than CAA, Visual Basic is easy to use and offers access to the major-ity of CAD/CAE features. A shortcoming of VBScripts is the lack of support for
ParametersRules
ControlRead
WriteInstantiate Run
Knowledge Patterns
UDFs VBScripts
Figure 16: Implemented automation concept
24
Part I: CAD/CAE-based mass estimation process
associative modeling. An example: If an object OA serves as an input for object OB, OA is associatively linked to OB. A modification of OA will now automati-cally trigger an update of OB. With VBScripts, the user is expected to manually manage the associative links of script-generated objects. This disadvantage is overcome by Knowledge Patterns as introduced by Ledermann et al. [29]. All objects generated by Knowledge Pattern scripts are stored in dedicated lists.
Wingspan(+30 %)
Sweep angle(-20°)
Chord length(-15 %)
Figure 17: Parametric-associative CAD model of an aircraft wing
25
2 Tools and methods
If an object in a list is replaced by the Knowledge Pattern script, the associative links are automatically updated and kept intact. A further automation capabil-ity is provided by UDFs (User Defined Features): UDFs allow parametrized geo-metrical entities of arbitrary complexity to be treated as stand-alone features. UDFs can be instantiated manually or automatically by Knowledge Patterns. Input parameters can be made public to allow for a customization of the instantiated UDFs. Both Knowledge Patterns and UDFs are part of the CATIA Knowledgeware environment.
2.4.2 Support of parametric associative modelingIn order to provide a broad design space, extensive parametrization of the aircraft and wingbox geometry models is essential. The technique used for the generation of the geometrical and structural models is described by the parametric-associative modeling concept [29]. A change in one parameter is automatically spread throughout the whole model (Fig. 17). The implementa-tion of this concept in CATIA V5 uses a combination of the automation tools described above. A Rule represents the top level control structure that trig-gers the Knowledge Patterns in a predefined sequence. The capabilities of the Knowledge Patterns are further enhanced by the complementary use of VBScripts and UDFs (Fig. 16).
2.4.3 Structural analysis capabilities (CAE/FEM)The CAE environment within CATIA V5 offers pre- and postprocessing ca-pabilities as well as a built-in FEM solver (Elfini). In order to use the structural sizer in combination with the stand-alone FEM solver Nastran, a bi-directional CATIA V5/Nastran gateway is required. This functionality is provided by the CATIA V5 add-on LMS Virtual.Lab Structures. It allows the automated import and export of FEM files in the proprietary Nastran file formats [43].
2.5 BLWF (CFD)
BLWF (Boundary Layer Wing Fuselage) is a CFD code developed at the Central Aerohydrodynamic Institute (TsAGI) in Moscow [44]. Based on potential flow theory, it allows the analysis of wing-body configurations in transonic flight with regard to viscous effects. A single CFD run including pre- and postpro-cessing can be performed in under two minutes (AMD Opteron 280 2.4GHz).
26
Part I: CAD/CAE-based mass estimation process
Code by language/type [LOC*]
Code by functionality [LOC*]
VBScripts(30%)
CAD generation(26%)
FEM generation(13%)
CFD generation(5%)
Postprocessing (5%)
Structural sizing(26%)
Load generation(18%)
Load application(7%)
Knowledge Patterns(20%)
Rules (1%)
MATLAB(49%)
* LOC = lines of code (total LOC = 33’758 lines)
MATLAB
CATIA V5
MATLAB
CATIA V5
Figure 18: Script statistics
27
3 Use of CAD/CAE functionality
Because of the high computational efficiency in comparison to higher fidelity CFD methods (e.g. Navier-Stokes equations as used in [45]), it is well suited for the use in initerative processes often found in aircraft pre-design. On the downside, BLWF has some limitations in combination with large angles of at-tack, as encountered during high-g maneuver loadcases, leading to premature flow separation and computational instabilities [46].
2.6 MATLAB
Custom scripts programmed in the technical computing language MATLAB are used for all tasks of the multidisciplinary process that can not be covered with CATIA V5. This includes the overall process control, the calculation and processing of the fuel loads, the processing of the aerodynamic loads, de-formation feedback during the aeroelastic coupling loop (FEM to CFD), the structural sizing and the postprocessing (numerical and visual) of the results.
2.7 Script statistics
An objective of this thesis was to make extensive use of CATIA V5 and its automation and scripting capabilities. Fig. 18 shows a statistical analysis of the custom scripts developed for the multidisciplinary process. The distribution of the scripts is measured in lines of code (LOC). It should be noted, that the number of LOCs is only a rough indicator of the software project size, as both the programming language and the programmers individual ability to write efficient code have a direct impact on this measurement. Nevertheless, it of-fers an interesting insight in the distribution of the scripts both by language and functionality. The upper chart reveals that half of the scripts are written in CATIA V5, with VBScripts and Knowledge Patterns accounting for most of the LOCs. The other half of the scripts are written in MATLAB. The lower chart shows the distribution of all LOCs by functionality (e.g. the generation of the CAD model).
3 Use of CAD/CAE functionalityThe following sections highlight the most important aspects of using the CAD/CAE software CATIA V5 as a multi-model generator for the mass estimation process.
3.1 Aircraft geometry model (CAD)
The primary application of CATIA V5 within the multidisciplinary process is the automated generation of the aircraft geometry model based on a set of user-defined input parameters. All other models, including the structural model and the models used for load generation, are based on the aircraft geometry model. The first step is the generation of the aircraft master geometry. Fig. 19 shows two different aircraft master geometries both based on the same CATIA V5 CAD template. All components of the master geometry assembly (wing, fuselage, empennage) are extensively parametrized to allow for a broad design space. The second step is the generation of the wingbox geometry integrat-ing ribs, spars and stringer-stiffened wing skins. All parameters used for the definition of the wingbox geometry are given in relative wing coordinates in accordance to the parametric-associative modeling approach. In a third step, the geometry models of the secondary structure (front and leading edges), the landing gear and the engines and their support structures are generated - again using relative wing coordinates wherever possible. The use of CATIA V5 for the generation of the aircraft geometry model offers several advantages: Firstly, it enables the generation of high quality surfaces (this is especially im-portant, as the CFD model is based on the geometry model), secondly, it leads to a reduction in development time by using the built-in CAD functionality of CATIA V5 and thirdly, it simplifies the exchange of geometry models through the use of industry standard data formats (e.g. CATPart, IGES, DXF).
3.2 Wing profile library (CAD)
The wing surface is defined by an arbitrary number of wing profile sections (spline curves). Every profile section requires the following input parameters: Spanwise location, airfoil shape, absolute chord length, relative profile thick-ness and profile twist angle. UDFs (User Defined Features) as described in sec-tion 2.4.1 were used for the implementation of the wing profiles in CATIA V5.
30
Part I: CAD/CAE-based mass estimation process
Slat geometry parametrization
Slat template instantiation
Input parameters: Position of the control points P1-P6
(in wing coordinates)
Slat template (UDF)
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Instantiation
# 1
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Front spar
Upper win skin
P5
P6 P4
P3P1
P2
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# 4
# 5# 6
# 7
Figure 20: Slat geometry generation
31
3 Use of CAD/CAE functionality
One parametrized UDF for every airfoil shape was created and stored in a dedicated wing profile library using the CATIA Catalog functionality. The use of Catalogs facilitates collaborative engineering, as they can be made available to multiple users and/or processes. During the generation of the wing surface, Knowledge Pattern scripts are used to automatically access the wing profile library, instantiate the airfoil UDFs and provide them with the appropriate input parameters.
3.3 Secondary structure (CAD/CAE)
The secondary structure includes the fixed and movable parts of the leading and trailing edges and accounts to the NSMs (non-structural masses) of the wing. In order to calculate the inertial loads caused by the secondary struc-ture, the mass of its components (e.g. the slats) needs to be determined. This is achieved with the help of predetermined weight functionals that give a component mass estimate based on the corresponding surface area [47]. A high accuracy of the weight functionals is very important as the secondary structure makes a significant contribution towards the total wing weight (up to 30-40% according to [9]).
Fully-retracted Fully-extended
85°
0°
Figure 21: Landing gear kinematics
32
Part I: CAD/CAE-based mass estimation process
Geometry model (CAD)
Structural model (CAE/FEM)
Unidirectionalassociativity
in CATIA
close-up
pylon struts(CBAR)
gear fittings(RBE3)
gear struts(CBAR)
engine fittings(RBE2/RBE3)
wingbox(CQUAD4, CTRIA3)
wingbox
landing gear
engines
pylon fairings
Figure 22: CAD/CAE associativity in CATIA V5
33
3 Use of CAD/CAE functionality
CATIA V5 is used for the following steps: Generation of the secondary structure geometry (CAD), determination of the surface areas and component masses (CAD), calculation and application of the inertial loads (CAE). Fig. 20 shows the generation of the slat geometries. One slat template (UDF) is sufficient for the generation of all slat instances. A slat instance is defined by the position of the six corner points (P1-P6) given in relative wing coordinates. The same approach is also used for the generation of the flaps, spoilers and ailerons.
3.4 Landing gear kinematics (CAD)
An advantage of UDFs is that their input parameters can be changed at any time. This is illustrated by the implementation of the main landing gear (Fig. 21). The gear retraction angle acts as an input parameter for the UDF and can be varied between 0° (fully-extended) and 85° (fully-retracted) in order to assess the landing gear arrangement and the packaging constraints. The same technique could also be used for the simulation of the flap and slat extension mechanisms.
3.5 Wingbox structural model (CAE/FEM)
A key feature of CATIA V5 is the unidirectional associativity between the geo-metrical (CAD) and structural (CAE/FEM) models. This means that changes in the CAD model are automatically reflected in the CAE/FEM model (Fig. 22). The FEM model of the wingbox is represented by quadrilateral and triangular shell elements (CQUAD4, CTRIA3). Stringers as well as the main landing gear structure and the engine supports are modeled with 1D bar elements (CBAR). The actual load introduction of landing gear and engine loads is performed with stiffening and non-stiffening interpolation elements (RBE2, RBE3). Spring elements (CLAS2) in combination with non-stiffening interpolation elements are used to create realistic wing root restraint conditions that allow for a cer-tain compliance in the areas where the wingbox is attached to the fuselage. The spring stiffness parameters were determined with the help of a second structural model that included both the wing structure and the center fuse-lage section [48]. The mesh size is variable and is defined by a separate input parameter. The standard mesh size of 200mm results in an FEM model with approximately 1·104 FEM elements and 4·104 DOFs (degrees of freedom).
34
Part I: CAD/CAE-based mass estimation process
CAD (CATIA V5)
CFD (BLWF)
Master geometry
Cutting plane
Scan direction
CFD surface meshCFD Pressure distribution (cp)CFD Pressure distribution (cp)
The automated use of the CFD solver BLWF for the calculation of the aerody-namic loads requires both export and import interfaces to be implemented in CATIA V5 [49]. The export interface provides BLWF with the necessary input parameters to carry out the CFD calculation. Most importantly, these input parameters include the aircraft geometry in the form of cross sections for the fuselage, the wings and the empennage. CATIA Knowledgeware tools, such as Knowledge Patterns and VBScripts, are used for the automatic retrieval of these cross sections by intersecting the aircraft geometry with a moving cut-ting plane (Fig. 23).
3.7 Fuel distribution (CAD)
Fuel loads are a significant contributor towards the total wing loads. The cal-culation of the fuel loads requires precise knowledge of the fuel distribution within the fuel tanks. With CATIA V5, an automatic method for the calcula-tion of the fuel distribution was implemented: During static loadcases, the fuel surface is always perpendicular to the acceleration vector. In an iterative process, the fuel height in every fuel tank is adjusted until a target fuel volume is reached. The upper half of Fig. 24 shows the center fuel tank and the cor-responding fill curve for this fuel tank during cruise flight. In the lower half, two fuel distributions for accelerations acting in vertical direction (top) and horizontal direction (bottom) can be seen. Also shown is the center of gravity for every fuel tank. As CATIA V5 lacks provisions for the generation of hydro-static pressure loads, a custom MATLAB script is used for the calculation of the hydrostatic fuel pressure loads acting on the fuel tank boundaries. In CATIA V5 these pressure loads are applied to the structural model with the help of the built-in surface loads mapping interface. The same pressure mapping function-ality is also used for the application of surface-distributed aerodynamic loads.
3.8 Flying shape reconstruction (CAD)
The aircraft geometry model features the wing in its undeformed shape, the jig shape. During static flight however, loads acting on the wing lead to a deformation of the wing surface and thus a new shape which is referred to as the flying shape. The flying shape is calculated with a weak fluid-structure
36
Part I: CAD/CAE-based mass estimation process
Calculation of the hydrostatic fuel height
Sample fuel distributions
hmin
hfuel
hmax
Fuel volume V
Acceleration vector a
Acceleration vector(2.5g maneuver loadcase)
COG
Center tank fuel (10.5m3)
Inboard tank fuel (13.5m3)
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Tip tank fuel (2.2m3)
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3 ]min
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target Fuel volume
resultingFuel height
Figure 24: Calculation of the fuel distribution in CATIA V5
37
4 Application and results
coupling method [31,50]: In an iterative process, the elastic deformation of the structural model (FEM) is first applied to the aerodynamical model (CFD). In a subsequent step, the resulting pressure distribution is applied to the structural model via the CATIA V5 loads interface. The aeroelastic equilibrium is usually found after 5-10 iterations. The geometry model of the wing surface remains unchanged during this process as the aerodynamical model is altered outside of CATIA V5. To enable further aerodynamic analysis after the calculation of the flying shape, a method for the reconstruction of the flying shape geometry was implemented in CATIA V5. By assuming that the wing profile sections remain undeformed and experience translation and rotation only, the existing wing geometry generator can be used. The position and twist angle of the profile sections are updated to reflect the flying shape. With this approach, a high quality geometry model of the flying shape can be generated and pro-vided for further analysis.
4 Application and results
4.1 Test case «DLR-F11 wingbox»
4.1.1 Aircraft configurationIn order to test the application potential of the multidisciplinary process, a mass estimation of the wingbox of a generic long range aircraft was per-formed. The wing shape of the test aircraft is based on the DLR-F11 con-figuration developed at the German Aerospace Center (DLR) [51,52]. With a wingspan of 53.4m, a fuselage length of 58.6m, an OWE (operating weight empty) of 106.8t and an MTOW (maximum take-off weight) of 230.3t, the test aircraft is comparable to an Airbus A330-200 in both size and weight. The MFW (maximum fuel weight) of 103.4t enables a theoretical maximum range of 10’350km (courtesy of Johannes Rieke, TU Braunschweig, Institute of Aircraft Design and Lightweight Structures). The wing planform, the structural layout and the arrangement of the secondary structure are shown in Fig. 13. FA front/middle/rear spar arrangement with wing ribs perpendicular to the front spar was used. The main landing gear is attached to the wingbox by means of a false rear spar structure.
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Part I: CAD/CAE-based mass estimation process
4.1.2 MaterialsThe current version of the mass estimation process is limited to isotropic mate-rials (e.g. aluminium alloys) as the automated generation of orthotropic mate-rials (e.g. CFRPs) is not fully supported by the latest release of CATIA V5 (r19). Two different aluminum alloys were used for the wingbox structure: High-strength aluminum 7050-T7451 for the upper skins/stringers and the spars and 2024-T351 alloy for the lower skins/stringers and the ribs. Although 7050-T7451 alloy offers superior strength characteristics, 2024-T351 alloy is better suited for components stressed by cyclic tensions loads and therefore prone to fatigue damage such as the lower wing skins and stringers. The material properties and allowables used for the structural sizing are listed in Tab. 1.
Table 1: Material properties and allowables (source: MatWeb)
4.1.3 LoadcasesHundreds of loadcases are used during the detailed design phase, but only a small number of them are relevant for the preliminary design. In this case, the aircraft was subject to eight static loadcases including maneuver, landing and crash loadcases (Tab. 2). The maneuver loadcases featured load factors be-tween 2.5g and 2.87g (limit load) with different fuel and payload configura-tions for every loadcase. Two landing loadcases with a load factor of 3.5g (limit load) were defined to simulate the impact loads during landing. Both landing loadcases included an aircraft at MLW (maximum landing weight), either with the maximum allowable payload or the maximum allowable amount of fuel. A cruise loadcase (1.0g) was used for the calculation of the flying shape of the wing. Finally, a crash loadcase simulating a horizontal crash at MTOW with a load factor of 6.0g (ultimate load) in flight direction was included for the in-vestigation of fuel load effects in combination with nodal load introduction.
4.1.4 Sizing criteriaTwo stress criteria and one buckling criterion were used for the structural siz-ing of the aluminum wingbox structure. The stress criteria used σyield at limit load and σultimate at ultimate load. The reserve factors were set to 1.0 (limit load) and 1.5 (ultimate load). The FEM-based buckling criterion considered limit load buckling with a target reserve factor of 1.0 at limit load. The post-buckling behavior was not analyzed.
4.2 Results
4.2.1 Weight breakdownA weight breakdown by weight chapter for both the primary structure (wing-box) and the secondary structure (leading and trailing edges) are shown in Tabs. 3 and 4. All values are given for the entire wing (tip-to-tip). The masses of the wingbox components result from physics-based mass estimation, whereas the masses of the secondary structure components are calculated with the help of weight functionals. The accuracy of the results is heavily influenced by the fidelity of structural model. In case of the ribs and spars, the resulting component masses should be taken with care, as the underlying structural models are comparably simple [53].
4.2.2 Sheet thicknessThe areas with the largest sheet thickness are found in the upper and lower wing skins near the wing kink (Fig. 29). These are the areas that experience the highest bending moments and shear stresses in relation to the chordwise depth and the thickness of the wingbox. During flight maneuvers with positive load factors, the upper wing skins experience mainly compression loads while the lower wing skins experience mainly tension loads. The opposite effect is observed during the landing impact: The upper wing skin is subject to tension and the lower wing skin is subject to compression. In the current version, the
41
4 Application and results
FEM-based buckling criterion is limited to the optimization of the sheet thick-ness values but not the stringer cross sections. This leads to an overestimation of the sheet thickness in the areas prone to buckling.
4.2.3 Dimensioning loadcase and sizing criterionThe plot of the dimensioning loadcase shows that the wing is mainly dimen-sioned by the maneuver and landing loadcases (Fig. 31). Both types of load-cases induce high bending moments in the order of 2·107 Nm and drive the sheet thickness of the wing skins. Locally, the landing impact loads are the main drivers for the thickness of the inner rear spar and ribs. An interesting effect is observed in combination with the crash loadcase: The thickness of the inner section of the front spar and the adjacent areas of the skins and ribs is determined by the fuel pressure loads experienced during the crash loadcase. The predominant sizing criteria are the ultimate load stress and limit load buckling criteria (Fig. 32).
4.2.4 Combined safety factorThe safety factor is a measure for the structural efficiency. A local safety factor of 1.0 indicates optimal material utilization. Safety factors > 1 indicate slack material (unless the minimum sheet thickness is reached) while safety factors < 1 show that the sheet thickness is insufficient and that the local sizing criteria can not be met. The combined safety factor shown in Fig. 30 represents the lowest local safety factor for all loadcases. The plot shows that the reserve fac-tor in most areas of the wingbox is equal or greater to 1.0. This suggests that the structure is safely dimensioned and structural efficiency is high.
4.2.5 Static aeroelasticity (flying shape)The flying shape during cruise flight is determined by the wing loads and the wing stiffness. The distribution of the pressure coefficient (Cp) is shown in Fig. 25. Detailed results of the flying shape calculation are shown in Fig. 26. With swept-back wings, bending-torsion coupling due to aerodynamic lift loads leads to a gradual reduction in profile twist angle in spanwise direction, referred to as washout. As a consequence, less lift is generated by the outer section of the wing. In order to compensate for this reduction in total lift, a higher angle of attack is required (α = 2.9° for the flying shape vs. α = 2.3° for the jig shape). The resulting inward shift of the aerodynamic lift is clearly visible when comparing the lift distributions for both the jig and flying shapes. This also leads to a reduction of the wing bending moment. However, the impact of the aeroelastic deformation on the structural weight of the wingbox was not analyzed, as the aeroelastic calculation was only performed for the 1.0g cruise loadcase but not for the dimensioning maneuver loadcases. This was due to limitations of the CFD tool BLWF in combination with high angles of attack.
4.2.6 Convergence behaviorThe structural mass of the wingbox was used for the analysis of the conver-gence behavior of the structural sizing process. As seen in Fig. 27, the struc-tural mass and the convergence behavior is heavily influenced by the choice of sizing criteria. When using stress criteria only or stress criteria in combination with an analytical buckling criterion, the structural sizing converges after 5 to 10 iterations. When using the novel FEM-based buckling criterion, more itera-tion steps are required and convergence is reached after 25 iterations.
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Part I: CAD/CAE-based mass estimation process
Buc
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Figure 28: Optimization of the buckling eigenvalues
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11’895
1 5 10 15 20 25
Figure 27: Convergence of the structural sizing process
45
4 Application and results
4.2.7 Buckling optimizationThe FEM-based buckling criterion adjusts the local sheet thickness in order to optimize the buckling eigenvalues. The buckling optimization is successful, when all eigenvalues λ for all loadcases are equal or greater to 1.0. Fig. 28 plots the lowest twenty eigenvalues for every loadcase over the whole structural siz-ing run. Although 968 potential buckling fields with individual thickness values are present in the structural model, a rapid shift of eigenvalues towards the target value of 1.0 can be observed during the first few iterations. Neverthe-less, the FEM-based buckling criterion offers room for further development, as some critical eigenvalues (λ < 1.0) persist even after completion of the structural sizing run.
4.2.8 Computational costThe computational cost for every step of the mass estimation process is shown in Tab. 5. The steps involving CATIA V5 are of special interest in order to assess the suitability of CATIA V5 for this process. The time used for the generation of the CAD, CAE/FEM and CFD model amounts to approximately one hour. An-other hour is required for the load generation and application. The time used for the structural sizing depends on the number of loadcases, the FEM model fidelity and the sizing criteria and could be further reduced by parallelization.
Dimensioning criterionUltimate load strength Min thickness
Limit load buckling Max thickness
Figure 32: Dimensioning sizing criterion
Figure 31: Dimensioning loadcase
48
Part I: CAD/CAE-based mass estimation process
4.3 Summary
The use of the CAD/CAE software CATIA V5 as a multi-model generator within the mass estimation process is successfully demonstrated. The core function-alities covered by CATIA V5 include the generation of the geometrical (CAD), structural (CAE/FEM) and aerodynamical (CFD) models.
A combination of the built-in automation capabilities of CATIA V5 involving Knowledge Patterns, VBScripts, UDFs and Rules is used for the implementation of these core functionalities. The remaining functionalities of the mass estima-tion process, notably the generation and processing of the wing loads, the FEM-based structural sizing and the postprocessing, are provided by custom MATLAB scripts. Measured in lines of code (LOC), approximately half of the total software development effort was spent on CATIA V5-based functional-ities with the other half spent on custom MATLAB scripts.
The proof of concept is given in the form of a case study featuring the mass estimation of the wingbox of a transport aircraft based on the DLR-F11 con-figuration.
Investigation of local load introduction methods for wing loads in pre-design
5 Introduction to Part IIThe second part of the thesis is dedicated to the investigation of local load introduction methods. The CAD/CAE-based mass estimation process supports two different load introduction methods: The first one uses low-fidelity SMT loads, the second one uses high-fidelity nodal loads. An overview of both load introduction methods as well as details regarding the load introduction mod-eling (FEM-specific aspects) are given in chapters 5.3 and 5.4. An extensive analysis of the two load introduction methods and their impact on the results of the mass estimation process is presented in chapter 6.
5.1 Physics-based mass estimation
Part II of the thesis sets out to compare different methods for the introduction of wing loads during aircraft pre-design. In order to answer the questions for-mulated in section 1.5, a physics-based multidisciplinary process for the mass estimation of transport aircraft wingbox structures was developed and used. As the multidisciplinary process is able to handle both SMT and nodal loads, a direct comparison between the two methods of load introduction can be performed.
5.2 Structural sizing
FEM (Finite Element Method) based structural sizing is a local optimization method. In an iterative process, the structural sizing algorithm adjusts the lo-cal FEM element properties (e.g. sheet thickness) of all sizing zones in order to meet a number of predefined sizing criteria. Fig. 34 shows a close-up of
52
Part II: Investigation of local load introduction methods
the actual FEM model of the wingbox used for this investigation. Both shape and topology of the structure remain unchanged during this process. Often used sizing criteria include stress, strain and buckling criteria. Fig. 33 shows an example of a fully stressed design of a wing skin obtained by structural sizing with a stress criterion. The initial uniform sheet thickness leads to both
2
30
20
10
15
5
25
0
700
400
200
300
100
500
600
Initial sheet thickness
Sizing
Sizing
Sheet thickness after sizing [mm]
[N/mm2]Initial stress (von Mises) Stress after sizing (von Mises)
Top skin(uniform thickness)
480
280
380
500
550
360
350
350
355
360
8
8
8
8
8
13
4
8
9
17
Even stressdistribution
(target: 360 N/mm2)
Max. stress
Max. thicknessFront spar
Ribs
xy
z
xy
z
Figure 33: Fully stressed design principle
53
5 Tools and methods
under- and overstressed areas. After structural sizing, the optimized thickness distribution results in an even stress distribution with stress levels near the maximum material allowables and therefore maximum structural efficiency.
5.3 Load introduction methods
Wing structures are subject to different types of loads: The most important types are aerodynamic loads, fuel loads, engine loads, landing gear loads and inertial loads of both structural and non-structural masses. This publication compares two different methods of load introduction that either use SMT or nodal loads.
A straightforward approach to handle wing loads is to express them as SMT (shear, moment, torsion) cut loads. SMT cut loads are always given in reference to a virtual load axis running through the wing in spanwise direction (Fig. 35). Three orthogonal pairs of forces and moments are used to represent the total free cut loads at every point along the load axis. Fig. 42 shows the SMT cut load curves for a typical 2.5g maneuver loadcase.
A
B
A
B
Front spar(2D shells)
Pylon structure(1D bars)Lower skin
(2D shells)
Top skin(2D shells)
Stringers(1D bars)
Rear spar(2D shells)
Ribs(2D shells)
xy z
Figure 34: FEM model detail (outer wing, 200mm mesh size)
54
Part II: Investigation of local load introduction methods
In order to be used for load introduction, SMT cut loads have to be processed first [54]: Incremental SMT loads that are suitable for load introduction are ob-tained by calculating the difference in SMT cut loads between two consecutive points on the load axis. The points where the SMT load axis intersects the wing ribs are used as SMT load application points. The actual load introduction into the wingbox structure occurs at the rib boundary curves. Non-stiffening load transfer elements (Nastran RBE3s) are used to connect the SMT load applica-tion points with the load introduction curves.
The fact that SMT loads are easy to process makes them suitable not only for the conversion of loads between different computational models but also for the use in load introduction.
The quest for increased accuracy in aircraft pre-design has stirred interest in nodal loads. They are called nodal loads because the loads are ideally directly applied to the individual nodes of the FEM model. As an example, aerodynamic loads acting on the wing surface can be represented by surface distributed pressure loads applied directly to the wing skins. Compared to SMT loads,
SMT loads
SMT axisRBE3s
S
TM
SMT loads
Rib
SparSMT points
SMT axis
x y
z
Figure 35: SMT loads
55
5 Tools and methods
nodal loads are more complex and require dedicated interfaces for different load types (e.g. engine support structures for the introduction of engine loads as illustrated in Fig. 39).
5.4 Load introduction modeling
5.4.1 Aerodynamic loadsAerodynamic loads are the most important loads for the design of the wingbox structure. Lift induced shear, bending and torsion loads are the main drivers for the dimensioning of the spars and the wing skins. The multidisciplinary process used for the mass estimation uses a CFD (computational fluid dynamics) tool based on potential flow theory for the calculation of the aerodynamic loads [44]. In case of SMT-based load introduction, all aerodynamic loads acting on
Surface pressure loads(wing skins)
Trailing edge nodal loads(rear spar)
Load introduction curve(rib/spar intersection)
RBE3s
Leading edge nodal loads(front spar)
x y
z
Figure 36: Aerodynamic loads (nodal loads)
56
Part II: Investigation of local load introduction methods
the wing are expressed as lumped forces and moments distributed along the SMT line as shown in Fig. 35. By contrast, nodal loads based load introduction makes use of a mix of pressure loads and lumped loads. Aerodynamic pressure loads acting on the primary structure of the wing (the top and bottom skins) are represented by surface distributed pressure loads. Depending on the load-case, significant aerodynamic loads are also acting on the secondary structure of the wing (the leading and trailing edges). As the secondary structure is not
0
0.3·105
0.1·105
0.2·105
0
3·105
1·105
2·105
Fuel pressure (2.5 g maneuver loadcase)
Front spar detail
nz = 2.5 g
Bottom skin
P [N/m2]
yx
z
y
z
x
Fuel pressure (6.0 g horiz. crash loadcase)
Max pressure
Max pressure
Front spar detail
nx = 6.0 g
Bottom skin
P [N/m2]
yx
z
y
z
x
Max pressure
Figure 37: Hydrostatic fuel pressure
57
5 Tools and methods
represented in the structural model of the wing, these loads are introduced as lumped loads attached to the spars of the wingbox. Loads affecting the leading edge are attached to the front spar while load acting on the rear spar are attached to the rear spar. Non-stiffening load transfer elements are used to connect the virtual load application points between the rib stations with the load introduction curves on the spars. Fig. 36 shows a close-up of the mid wing section with both pressure loads and lumped loads applied. As the CFD tool used is limited to the processing of clean aircraft configurations only, the calculation of the aerodynamic loads acting on the high-lift devices during take-off and landing [55] is not possible at the current stage. For this reason, the structural model does not feature the explicit modeling of load-carrying structures in the form of slat or flap tracks.
5.4.2 Fuel loads
Accelerationvector
Fuel tank 1(center)
Fuel tank 2(inboard)
Front spar
Fuel tank boundary rib
Hydrostatic fuel pressure(pressure mapping on wingbox)
Upper skin
Fuel tank 3(outboard)
xyz
Figure 38: Fuel loads (nodal loads)
58
Part II: Investigation of local load introduction methods
Depending on the loadcase, fuel loads can lead to both an increase or a de-crease in total wing loads. During ground handling (e.g. pressure fueling), taxi maneuvers or rapid acceleration or deceleration fuel stored in integral wing tanks can lead to hydrostatic pressure loads acting on the wingbox structure. During stationary flight maneuvers, fuel loads typically counteract aerody-namic lift loads and thus lead to a decrease in total wing loads [56]. This load relief effect can be seen in Fig. 42 where the fuel loads lead to a significant reduction in shear, bending and torsion loads. As with aerodynamic loads, fuel loads can be introduced as SMT loads at the wing rib stations. In the case of nodal loads however, fuel loads are modeled as surface distributed hydrostatic pressure loads acting directly on the wingbox structure (Fig. 38). Hydrostatic pressure is a function of the hydrostatic height (fuel level), the fuel density, the acceleration and the ambient pressure. The pressure distribution therefore depends on both the fuel tank layout and the fuel distribution which varies as fuel is consumed during the flight.
5.4.3 Engine loadsEngine loads include both thrust and inertial loads. In case of underwing engine installations, the inertial loads lead to a similar load relief effect as experienced with fuel loads. Four main components provide the mechanical interface between the wingbox and the pylon structure: Two forward brackets (front fittings), a thrust spigot and a rear mounting bracket (aft fitting). The forward brackets are attached to the forward face of the front spar. They are connected to the forward lugs of the pylon via links and take vertical loads only. The thrust spigot is located at the bottom flanges of the forward brackets and interfaces with the top deck of the pylon. The spigot takes thrust and side loads only. The rear mounting bracket is located aft of the forward brackets on the underside of the wingbox. To ensure a statically determinate mounting system, the rear mounting bracket takes vertical and side loads only. Fig. 39 shows a drawing of the actual engine loads interface used for nodal loads introduction. The front fittings, the thrust spigot and the aft fitting are mod-eled with a combination of stiffening (RBE2) and non-stiffening (RBE3) load carrying elements. The pylon structure is represented by a truss structure made of 1D bar elements (CBARs). In order to reduce model complexity, both thrust and inertial loads are applied at the same point - this is not necessary the case in reality. A further simplification applies to the aft fitting which attaches di-rectly to the bottom wing skin. In reality, intercostals between neighboring ribs
59
5 Tools and methods
are sometimes used as attachment points for the aft fittings. When introduced as SMT loads, the engine loads are represented by SMT loads distributed across the three nearest load introduction points on the SMT axis.
Thrust loads
xy
z
Load introduction point
Inertial loads
Front fittings(inertial loads)
Pylon struts
Spigot(thrust loads)
Aft fitting(inertial loads)
Pylon fairing
Upper wing skin
Front spar
Figure 39: Engine loads (nodal loads)
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Part II: Investigation of local load introduction methods
5.4.4 Landing gear loadsThe implementation of the nodal landing gear loads is shown in Fig. 40. The landing gear is modeled as a truss structure attached to the wingbox structure through three separate fittings: The front and aft trunnion fittings and the
Double bogie
Load introduction point
Main leg
Landing gear load
Sidestay
Rear spar Side brace
Trunnion
Aft trunnion fitting (RBE3)
False rear spar structure
Drag strut
Fwd trunnion fitting (RBE3)
Upper wing skin
Sidestay fitting (RBE3)
x y
z
Figure 40: Landing gear loads (nodal loads)
61
6 Application and results
sidestay fitting. A false rear spar structure attached to the rear spar provides the aft pick-ups for the landing gear. The false rear spar structure is respon-sible for introducing the drag and bending loads into the wingbox structure. All fittings are modeled with non-stiffening load carrying elements (RBE3s). When introduced as SMT loads instead of nodal loads, the landing gear loads are represented by SMT loads placed on the four nearest SMT load introduc-tion points.
5.4.5 Non-structural massesNon-structural masses (NSMs) account for leading and trailing edge compo-nents attached directly or indirectly to the wingbox structure. The most impor-tant NSMs include flaps, slats, spoilers, ailerons, fairings and falsework. The same load interfaces at the front and rear spar are used for the load introduc-tion of the aerodynamic loads acting on the secondary structure are used for the introduction of the NSM inertial loads (Fig. 41). As an example, the inertial loads caused by the aileron mass are distributed to the load application points on the rear spar directly in front of the aileron. In case of SMT load introduc-tion, load application points on the SMT axis are used instead. A similar ap-proach for the attachment of NSMs is also featured in [57].
NSM inertial load
Load introduction points
RBE3 elements
Aileron surface
NSM nodal loads
Rear spar
Leading edge
Non structural mass (NSM)
Front spar
xy
z
Figure 41: Non-structural masses (nodal loads)
62
Part II: Investigation of local load introduction methods
5.4.6 Structural massesInertial loads of the wingbox structure are automatically accounted for during the FEM structural analysis by applying a static acceleration vector. The use of SMT loads for this load type was not implemented, because the inertial loads depend on the mass distribution which is subject to constant change during the iterative structural sizing process.
6 Comparison of different load introduction methods
6.1 Test case «DLR-F11 wingbox»
6.1.1 Aircraft configurationA generic long range aircraft with a wingspan of 53.4m and an MTOW (maxi-mum take-off weight) of 230.3t was used for this study. The wing shape is based on the DLR-F11 configuration developed at the German Aerospace Cen-ter (DLR) [58]. The wingbox is a conventional all-aluminium structure made of spars, ribs and stringer-stiffened wing skins. Aluminium alloys used are 7050-T7451 (spars, upper skin) and 2024-T351 (ribs, lower skin). Four integral fuel tanks result in a maximum wing fuel capacity of 103.4t.
6.1.2 LoadcasesA total number of eight loadcases were used for the test case (Tab. 2, Part I of this thesis). Depending on the loadcase, the total aircraft mass varied between 150.9t (maximum zero-fuel weight) and 230.3t (maximum take-off weight). Besides maneuver and landing loadcases, a horizontal crash loadcase was used to account for the effects of rapid deceleration in flight direction during take-off at MTOW.
6.1.3 Sizing criteriaAlthough the structural sizer supports stress, strain, fatigue and buckling cri-teria, only two stress criteria for limit and ultimate load were used (see appen-dix C «Fatigue» for an analysis of the impact of fatigue on structural mass). Initial tests showed that the use of analytical buckling criteria led to an overall
63
6 Application and results
-3e6
-2e6
-1e6
1e6
0
0eta [-]
Shea
r for
ce (S
) [N
]
0.2 0.4 0.6 0.8 1
0eta [-]
0.2 0.4 0.6 0.8 1-4e7
-3e7
0eta [-]
0.2 0.4 0.6 0.8 1
-2e7
-1e7
0
1e7
Ben
ding
mom
ent (
M) [
Nm
]
-6e5
-2e5
-4e5
4e5
2e5
0
Tors
ion
mom
ent (
T) [N
m]
Total torsion moment (T)Engines
FuelSM
AeroNSM
Total shear force (S)
Aero
Engines
NSMSM
Aero
Total bending moment (M)
Fuel
NSMSMEngines
Fuel
Figure 42: SMT cut loads (maneuver loadcase 2.5g)
64
Part II: Investigation of local load introduction methods
increase in structural mass of 13% but tended to obscure the effects of local load introduction. It is thus important to remember that the mass estimates presented in the results section should be used for the comparison of different load introduction methods only.
6.2 Results
The results were gathered in three steps: Firstly, an overall comparison be-tween SMT and nodal loads introduction was performed by exclusively using SMT or nodal loads only. Secondly, load type specific effects were analyzed by alternating the load introduction method for single load types one after another. Thirdly, the influence of the FEM mesh size on the results of the mass estimation process was analyzed. All results are given in reference to the entire
aircraft wing (tip-to-tip).
(All load types active)Sized thickness A Sized thickness B Delta thickness A-B
(All but gear loads active) (gear load specific effect)
t [mm]
2
30
20
10
t [mm]
2
30
20
10
t [mm]18
0
5
15
10
Figure 43: Isolation of load type specific effects on sheet thickness
65
6 Application and results
6.2.1 SMT vs. nodal load introductionThe use of nodal loads instead of SMT loads for load introduction resulted in an overall increase in structural mass of 4% (Tab. 6). Snowball effects leading to a further decrease in structural mass by reducing the overall aircraft loads were not accounted for. The corresponding thickness distributions and the increase in sheet thickness resulting from the use of nodal load introduction are shown in Figs. 49-51. Differences in sheet thickness are visible in the following areas: The inner section of the front spar and the adjacent areas of the wing skins, the section of the wingbox surrounding the main landing gear attachment and part of the front spar and lower wing skin used for the attachment of the engines.
6.2.2 Impact of load introduction modeling by load typeThe following approach was chosen to isolate the effects of the individual load types: Starting with SMT loads for all load types, the load introduction method was gradually changed to nodal loads for every load type until all load types used nodal loads only. Fig. 44 shows the individual contribution of every load type towards the total mass increase experienced when using nodal loads only. The biggest impact on structural mass can be attributed to the use of nodal loads introduction for fuel and landing gear loads. By contrast, the use of nodal loads introduction for aerodynamic and engine loads resulted in
66
Part II: Investigation of local load introduction methods
a comparably low increase in structural mass. In order to find an explanation for the observed mass increase, the individual impact on thickness distribution was calculated for every load type.
6.2.3 Impact of aerodynamic loadsAnalysis showed that the 2.5g maneuver loadcase (#4) is the single most important loadcase for the dimensioning of the wingbox. The biggest part of the shear forces and bending moments acting on the wingbox structure are caused by the aerodynamic lift loads. Surprisingly, the use of nodal load introduction for aerodynamic loads resulted in a comparably low increase in wingbox mass of 0.5% (Tab. 7). This suggests that aerodynamic loads are ac-curately represented by SMT loads.
Win
gbox
mas
s [kg
]
All loa
ds SMT
Aero lo
ads n
odal
Fuel lo
ads n
odal
Engine
load
s nod
al
Gear lo
ads n
odal
NSM load
s nod
al
All loa
ds no
dal
12’600
12’0
32kg
12’5
16kg
+63kg
+214kg+60kg
+152kg -5kg
12’200
12’400
11’800
12’000
11’900
12’100
12’300
12’500
Figure 44: Impact of nodal loads on wingbox mass by load type
Table 7: Impact of aero loads modeling (SMT vs. nodal loads)
6.2.4 Impact of fuel loadsThe use of nodal loads introduction for fuel loads led to a significant increase in structural mass (Tab. 8). The direct impact of the fuel loads on the thickness distribution of the wingbox is shown in Fig. 45.
Table 8: Impact of fuel loads modeling (SMT vs. nodal loads)
Two effects can be observed: Firstly, for both load introduction methods, fuel loads lead to a load relief effect (decrease in wing shear force and bending moment) during the maneuver loadcases and consequently a reduction in sheet thickness in the upper and lower wing skins. A more detailed review of this load relief effect, with a focus on the defuelling sequence, is given in Appendix B of this publication. Secondly, it is the horizontal crash loadcase
68
Part II: Investigation of local load introduction methods
(#8) which leads to a build-up of hydrostatic pressure loads (up to 3 · 105 Pa) and high stress levels in the front spar and the adjacent areas of the upper and lower wing skins. This leads to a significant increase in sheet thickness in both the inner front spar and the forward sections of the inner wing skins. This increase in sheet thickness due to fuel pressure loads cannot be observed when using SMT loads.
SMT load introduction
t [mm]
Nodal loads introduction
-8
10
8
6
4
0
-4
-2
-6
2
False rear spar
Thickness increasedue to local pressure loads
(crash loadcase)
Thickness decrease
Upper wing skin
x
y
z
Figure 45: Change in sheet thickness due to fuel loads
69
6 Application and results
6.2.5 Impact of engine loadsDuring maneuver loadcases, inertial engine loads lead to a reduction in overall wing loads and thus a reduction in structural mass. This load relief effect can be observed with both load introduction methods. However, the use of nodal load introduction for engine loads leads to a further increase in wingbox mass (Tab. 9). The increase in structural mass concerns mainly the lower wing skin and the front spar (Fig. 46) and is caused by inertial engine loads during the 3.5g landing loadcase (#3) and the horizontal crash loadcase (#8). A direct im-pact of the thrust loads on the thickness distribution could not be observed.
SMT load introduction
t [mm]
Nodal loads introduction
-2
20
16
18
14
12
8
4
6
2
0
10
Aft engine attachment
Thickness increasedue to engine loads
Fwd engine attachment
Lower wing skin
Front spar
xy
z
Figure 46: Change in sheet thickness due to engine loads (outboard eng.)
70
Part II: Investigation of local load introduction methods
Table 9: Impact of engine loads modeling (SMT vs. nodal loads)
6.2.6 Impact of landing gear loadsWhen introduced as nodal loads, landing gear loads led to a significant in-crease in structural mass (Tab. 10). The largest increase in sheet thickness was observed in the areas surrounding the main landing gear attachments (Fig. 47). The resulting mass increase mainly affected the inner rear spar and the adjacent areas of the upper and lower wing skins. A comparable increase in local sheet thickness could not be observed when using SMT loads.
Table 10: Impact of landing gear loads modeling (SMT vs. nodal loads)
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6 Application and results
6.2.7 Impact of NSM loadsThe use of nodal loads for the introduction of NSM loads (e.g. inertial loads caused by flaps, slats or spoilers) did not result in a significant change in struc-tural mass (Tab. 11). This is not surprising as the contribution of the NSM loads towards the total wing loads is relatively small as visualized in Fig. 42.
SMT load introduction
t [mm]
Sidestay attachment
False rear spar
Upper wing skin
Main leg attachment
Nodal loads introduction
-2
18
16
14
12
10
6
2
4
0
8
Sidestay attachment
False rear spar
Upper wing skin
Main leg attachmentx y
z
Figure 47: Change in sheet thickness due to landing gear loads
72
Part II: Investigation of local load introduction methods
Table 11: Impact of NSM loads modeling (SMT vs. nodal loads)
6.2.8 FEM mesh size sensitivityExternal loads can lead to stress concentrations near the points of load intro-duction (e.g. the engine fittings). The smaller the mesh size, the better the FEM model is able to capture these local effects. On the other hand, very fine meshes lead to unfavorably high CPU times for the structural analysis. As the FEM stress distribution drives the structural sizing, a parameter study was performed to study the impact of the FEM mesh size on the wingbox mass (Fig. 48). Another constraint that applies to the mesh size is given by the structural arrangement: The maximum mesh size is limited by the struc-tural arrangement, mainly the number and position of the ribs and stringers. As a consequence, the mesh size was varied between 100mm and 400mm. Two effects could be observed: Firstly, an increase in FEM mesh size led to a decrease in wingbox mass. Secondly, the relative difference in mass for both load introduction methods remained almost constant for mesh sizes between 100mm and 300mm. Therefore, the mesh size of 200mm used for this study seems reasonable, as it offers good enough accuracy paired with acceptable computational cost.
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6 Application and results
6.3 Summary
Part II focuses on the comparison of two different load introduction meth-ods for wing loads during aircraft pre-design. The methods implemented in the CAD/CAE-based multidisciplinary mass estimation process either use low-fidelity SMT loads or high-fidelity nodal loads. Both methods are introduced and their specific advantages and disadvantages are discussed. Based on the case study introduced in Part I, the two methods are compared with regard to their specific impact on the results of the mass estimation process. A detailed analysis, both qualitatively and quantitatively, is performed and recommenda-tions regarding the use these load introduction methods is given. The switch from SMT loads to nodal loads results in an overall increase in structural mass of the wingbox of 4% (484 kg). The biggest contributions originate from the use of nodal load introduction for fuel loads, landing gear loads and engine loads. The use of nodal loads introduction for aerodynamic loads resulted in a surprisingly low increase in structural mass of 0.5% (63 kg).
∆ mass [%]
Mass (nodal loads) [kg]
Mass (SMT loads) [kg]
Win
gbox
mas
s [kg
]
Rel
ativ
e m
ass d
iffer
ence
(nod
al v
s. sm
t) [%
]13’000
12’000
11’500
11’000
5.0
4.0
3.0
2.0
12’500
1.0
0.0100
Mesh size [mm]
200 300 400
Figure 48: FEM mesh size vs. wingbox mass
74
Part II: Investigation of local load introduction methods
Sheet thickness [mm]
2 302010 155 25
Sheet thickness [mm]
2 302010 155 25
Figure 50: Sheet thickness (nodal loads)
Figure 49: Sheet thickness (SMT loads)
75
6 Application and results
Sheet thickness increase [mm]
-15 155-5 0-10 10
Figure 51: Sheet thickness increase (Nodal vs. SMT loads)
An FEM-based buckling criterion for the structural sizing of shell structures
7 Introduction to Part IIIThe third and final part of this publication deals with a small but interesting aspect of the mass estimation process: The FEM-based structural dimension-ing, or more precisely, the buckling criterion used for the buckling optimiza-tion of the wingbox structure. The need for an improved buckling criterion for shell structures became apparent during the development of the proprietary structural sizer used for the dimensioning of the wingbox structure and con-sequently resulted in the development and implementation of the FEM-based buckling criterion.
7.1 Types of structural optimization
During the design phase of lightweight structures, engineers are often con-fronted with the task to maximize the structural efficiency. This means that the weight of the structure has to be kept to a minimum while constraints on strength, stability, or stiffness have to be fulfilled. Computational optimization methods are one way to tackle this problem. They can be classified into three distinct categories: Topology, shape and sizing optimization.
Topology optimization allows the addition or removal of individual structural entities while retaining the outer shape of the structure. In contrast to topolo-gy optimization, shape optimization keeps the initial topology but changes the shape of the exterior and/or interior domain of the structure. The third distinct category of structural optimization is described by sizing optimization: Sizing optimization allows only for changes of the local properties of a structure. In case of the truss structure shown in Fig. 52, these properties can include the cross section type and area of the interconnecting struts. Applied to shell struc-
78
Part III: FEM-based buckling criterion for structural sizing
Original structure
A)
B)
C)
D)
Topology optimization
Shape optimization
Sizing optimization
F
F
F
F
Figure 52: Types of structural optimization
79
7 Introduction
tures, sizing optimization includes the adjustment of shell properties, such as material type or sheet thickness. In theory, the combination of topology, shape and sizing optimization offers the best optimization results because it covers a broad solution space. A good example of a combined topology/shape optimi-zation followed by a sizing optimization used for the optimization of an aircraft structure can be found in [59]. An alternative approach for the integration of topology, shape and sizing optimization is described in [60]. In practice, full-fledged combined optimizations are rarely performed during the preliminary design phase because of either excessive computational expense or restrictions towards changes in topology and shape. In that case, structural sizing is a way to optimize the structure with a comparatively low computational effort.
7.2 Structural sizing
As shown in Fig. 53, structural sizing is an iterative dimensioning process. In a first step, the structure is manually or automatically divided into a number of sizing zones. Each zone can be allowed to have a different thickness within predefined upper and lower boundaries. In a next step, the sizing criteria that will be used during the optimization have to be defined. Most commonly used criteria include stress, strain and buckling (stability) criteria. After the structural analysis, the new thickness of every sizing zone is set by minimizing the local reserve factor. In case of the fully stressed design approach, this means that every sizing zone should be as highly stressed as possible while fulfilling the material allowables, operational requirements and manufacturing constraints. This iterative process is continued until the thickness distribution in the sizing zones converges and predefined stopping criteria are fulfilled. Because struc-tural sizing is a local optimization method, the resulting thickness distribution does not necessarily reflect the most optimal design but in most cases a suf-ficiently good design. During the last decades, structural sizing has been used with great success for the design of lightweight structures, e.g. during the preliminary design phase of aircraft structures [9,19,29].
7.3 The need for an improved buckling criterion
Analytical buckling methods are the state of the art for the calculation of the buckling reserve factors used for the structural sizing. They provide an ana-lytical solution to a specific buckling problem for a limited range of plate or
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shell geometries. Among other things, this problem is defined by the buckling field geometry, its boundary constraints and the loads acting on the buckling field. As a consequence, this means that during the structural sizing process, a suitable analytical solution has to be chosen for every buckling field in the structural model. Because this is not always possible, it is common practice to reduce all buckling problems to a handful of basic buckling problems. Depend-ing on the simplifications made, this practice can significantly compromise the accuracy of the structural sizing process. The author will subsequently
Sizing zone detection
Adjust zone thickness
Input (structure, parameters)
Structural analysis (FEM)
Convergence?
yesno
Evaluate sizing criteria
Output (sized structure)
Sizi
ng lo
op
Figure 53: Iterative structural sizing
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8 Sizing criteria for thickness sizing
introduce the concept of the FEM-based buckling criterion to handle an almost unlimited variety of buckling problems found during the thickness optimiza-tion of shell structures.
The following section gives an introduction to sizing criteria starting with a simple stress criterion. After that, the existing analytical buckling criterion and the new FEM-based buckling criterion are explained in sections 8.2 and 8.3. The implementation and application of the new FEM-based buckling criterion are described in chapter 9. An aircraft rudder serves as a test model to compare the performance of the two buckling criteria. Section 9.3 concludes the pres-ent work and offers an outlook on possible enhancements of the FEM buckling criterion. In its current form, the present work refers to structural sizing of shell structures with isotropic materials only.
8 Sizing criteria for thickness sizingDuring the structural sizing process, different sizing criteria are used to assess the reserve factors of the structure and its individual sizing zones. In order to maximize the weight efficiency of the structure, the individual reserve factors need to be minimized. A reserve factor FR = 1 means that the structure fulfills the sizing criteria and is sized adequately. In order to calculate the sized shell thickness, the correlation between shell thickness and the local reserve factor needs to be estimated. The most basic assumption is that the reserve factor is directly proportional to the shell thickness:
FR ∝ t (1)
Together with a global safety factor FS, the sized thickness can now be calcu-lated with the following formula:
(2)tsized = tinit ·FS
FR
with
(3)tmin ≤ tsized ≤ tmax
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The variable tinit denotes the initial sheet thickness and tsized denotes the sized sheet thickness after the sizing criteria are applied. The values tmin and tmax stand for the upper and lower limits for the sheet thickness, also called side constraints. We assume that the sheet thickness can be varied freely within these limits. In the real world, available sheet thickness values may be subject to manufacturing, process or cost constraints. In case of multiple sizing crite-ria or loadcases, the thickness sizing is performed individually for every sizing criteria and loadcase. The final sheet thickness for every sizing iteration step is determined by the highest individual thickness value. Before we start with the buckling criteria, we shall have a look at a basic stress criterion:
8.1 Von Mises stress criterion
A criterion often used for the dimensioning of sheet metal structures is the Von Mises stress criterion. By using this criterion, the sheet thickness of each sizing zone is adjusted until the resulting local stress value equals a target stress value. The target stress value is typically the maximum allowed stress value di-vided by a safety factor FS. The local stress values required by the criterion can either be determined analytically or with computational methods like the FEM method. The structural sizer described in section 7.2 relies solely on the FEM method. Let σinit be the initial stress value within a sizing zone. The maximum allowed stress is given by σmax. Because the exact correlation between the sheet thickness and the resulting local stress value is not known, we assume that the stress value is inversely proportional to the sheet thickness. This leads us to the following simple formula for the calculation of the reserve factor FR,vm and the sized thickness tsized:
(4)FR,vm =σmax
σinit
(5)tsized = tinit ·FS
FR,vm
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8.2 Limitations of analytical buckling criteria
Although analytical buckling methods are well understood, easy to apply and computationally inexpensive, there are some limitations: The formulas used for the calculation of the critical buckling loads are only valid for specific buck-ling problems. This includes the shape of the buckling field, the loads acting at the edges of the buckling field and the restraining boundary conditions. Furthermore, interaction between adjacent buckling fields can lead to global buckling modes which are very hard if not impossible to predict with analyti-cal methods
8.3 FEM-based buckling criterion
To overcome the limitations associated with analytical buckling methods, the present work suggests the use of FEM buckling analysis for the calculation of the buckling reserve factors.
8.3.1 FEM buckling analysisFEM buckling analysis can be performed with two methods: Either with an eigenvalue buckling analysis or with a nonlinear buckling analysis. Although the latter method is generally more accurate, it is also computationally more expensive. Because structural sizing is an iterative process and often used dur-ing the preliminary design phase, it is important to keep the computational cost of the buckling analysis as low as possible. This is why the present work focuses on the use of the faster but less accurate eigenvalue buckling analysis. The fundamental concept of the eigenvalue buckling analysis is to solve the following eigenproblem:
(16)[K] {vk} = λk [D] {vk}
where [K] is the stiffness matrix of the structure, [D] is the differential stiff-ness matrix, [vk] is the eigenvector (buckling mode) and λk the eigenvalue (buckling factor) of the buckling problem. If the FEM buckling criterion is used in combination with an FEM-based stress criterion, the stiffness matrix [K] is already available as a by-product of the FEM stress analysis. The results of the FEM buckling analysis include the eigenvectors v and eigenvalues λ for all
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requested buckling modes of the buckling problem. The eigenvalue λ equals the critical buckling factor which is the critical buckling load Fcrit divided by the actual load F:
(17)λ =Fcrit
F
8.3.2 Buckling criterion based on FEM buckling analysisSizing criteria for buckling optimization work by minimizing the buckling re-serve factor of every sizing zone (buckling field). The basic idea of the FEM-based buckling criterion is to use the results of the FEM buckling analysis for the calculation of these buckling reserve factors. This is done in two steps: Firstly, the retrieval of the critical eigenvalues for every sizing zone, and sec-ondly, the calculation of the new zone thicknesses.
Retrieval of the critical eigenvaluesThe results of the FEM buckling analysis include the eigenvectors and eigen-values of every buckling mode analyzed. The eigenvectors are represented by nodal displacement vectors d for every node of the FEM model. The maximum nodal displacement dnorm in every buckling mode is normalized to one length unit (e.g. 1mm). To find out which buckling fields are prone to buckling, the maximum displacement dmax in every buckling field is retrieved for every buckling mode calculated. An arbitrary minimum displacement threshold dcrit is used to identify the critical buckling fields:
(18)dcrit = 0.1 · dnorm
All buckling fields with a maximum node displacement dmax ≥ dcrit are re-garded as critical buckling fields. In order to decide, whether the thickness of a critical buckling field needs to be increased or decreased, a measure of the local buckling reserve factor is needed. This measure is given by the lowest eigenvalue λk of all buckling modes that triggers a critical node displacement in this field (Code 1).
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// Loop through eigenmodes FOR k=1 TO eigenmodes // Get max displacement of // eigenvector k in zone i d_max = max(eigenvector_k, i) // Check if buckling is significant IF d_max >= d_crit // Buckling is significant // Critical eigenvalue is of mode k lambda_crit = lambda_k ELSE // Buckling is not significant IF (k == last_eigenmode) // No buckling in zone i for all eigenm. return ELSE // Check other eigenmodes k = k + 1 END IF END IF END FOR
Code 1: Determination of the critical eigenvalue
Thickness calculationNow that the critical buckling fields and the critical eigenvalues λcrit are identi-fied, their thickness needs to be adjusted. An approximate relationship be-tween the eigenvalues and the thickness can be derived from the analyti-cal buckling formulas (appendix D). The critical buckling load is given by the product of the critical buckling stress σcrit and the cross section area of the buckling field:
(19)Fcrit = σcrit · tb = kEt3
b
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It can be seen that the critical buckling load is proportional to the power of three of the thickness.
(20)Fcrit ∝ t3
If we want to achieve a target eigenvalue λtarget after sizing, the new thickness can be calculated with the following equation:
(21)tsized = tinit ·3 λtarget
λcrit
A modified version of this equation is used for the thickness sizing of the buck-ling fields. Depending on the critical eigenvalue λcrit, the new zone thickness tsized is calculated as follows:
0 < λcrit < 1: Buckling fields in this category are undersized and are subject to buckling. Consequently, their thickness needs to be increased. To improve the convergence behavior of the iterative sizing process, the thickness increase is multiplied by a relaxation factor frelax (0 < frelax ≤ 1). Furthermore, the buckling intensity of the individual buckling field is taken into account by multiplying the thickness increase with the maximum node displacement dmax divided by the normalized node displacement dnorm.
(22)tsized = tinit + tinit
λtarget
λcrit− 1
· dmax
dnorm· frelax
1 ≤ λcrit ≤ 1.02: Buckling fields with a critical eigenvalue equal to or slightly above the target eigenvalue are well dimensioned. Their thickness does not need to be adjusted.
(23)tsized = tinit
1.02 < λcrit: Buckling fields with a critical eigenvalue greater than the target eigenvalue are oversized. Their thickness needs to be reduced in order to mini-mize the mass. The decrease in thickness is again damped with the relaxation factor frelax.
(24)tsized = tinit + tinit
λtarget
λcrit− 1
· frelax
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8 Sizing criteria for thickness sizing
No λcrit found: For some buckling fields, a critical eigenvalue might not be found. This means that none of the calculated eigenmodes lead to a critical node displacement in any of these buckling fields. There are two explanations for this: The first explanation is that buckling in these fields would occur, but only for eigenvalues higher than the maximum eigenvalue calculated. The second explanation is that these buckling fields are not critical to buckling (e.g. buckling fields under pure tension loads) and critical eigenvalues thus don’t exist. To distinguish between these two cases, the previous sizing iterations are analyzed to check whether or not critical eigenvalues ever existed for these buckling fields. If critical eigenvalues existed, then the new zone thicknesses are set to the sized zone thicknesses tpast of these very iterations.
(25)tsized = tpast
In case that no critical eigenvalues existed during the past iterations, it is as-sumed, that these fields are not prone to buckling. Consequently, their sized thickness is not determined by the buckling criteria but by other sizing criteria (Code 2).
// Import results of FEM buckling analysis // (eigenvectors, eigenvalues) importFEMResults() // Loop through sizing zones FOR i=1 TO zones // Evaluate zone eigenvectors evaluateZoneEigenvectors() // Handle zone buckling IF zone_buckling == TRUE // Zone is buckling // Adjust zone thickness acc. to eigenv. t_new = calc_thickness(t_old, lambda_crit) ELSE // Zone is not buckling // Check if buckling occurred in the past
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IF past_zone_buckling == TRUE // Use past zone thickness t_new = t_past ELSE // Do not adjust thickness END IF END IF END FOR
Code 2: Buckling field thickness adjustment
8.3.3 ImplementationThe FEM-based buckling criteria have been implemented in an existing struc-tural sizing framework. Already implemented sizing criteria include stress and strain criteria and an analytical buckling criterion based on the methods de-scribed in section 8.2. The framework is programmed in MATLAB and is able to perform structural sizing of MSC Nastran FEM models (BDF file format). The supported element types include two-dimensional quadrilateral and triangular shell elements (CQUAD4, CTRIA3) and one-dimensional bar elements (CBAR). As far as the sizing of bar elements is concerned, only stress and strain criteria, but no buckling criteria, can be applied to them. At the moment of writing, only isotropic materials (MAT1) are supported. The structural sizer is able to handle models with multiple static loadcases.
Input filesAs input files, a configuration file and an FEM input file for every loadcase are required. The FEM input file includes the FEM model definition (nodes, ele-ments, properties, materials, restraints, loads). The configuration file holds all the information necessary for the structural sizing process. This includes the definition of the sizing zones, the active sizing criteria, material allowables, thickness allowables and various process parameters such as termination cri-teria.
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Output filesAt the end of the structural sizing run, FEM input and output files of the sized structure are generated. Depending on the level of detail requested, the FEM output file holds the element-specific results of the static analysis and the buckling analysis. These results are available in the form of element stress and strain values and nodal displacement vectors. Furthermore, all the information generated during the structural sizing process is stored in a separate MATLAB output file. Among other information, this includes the thickness distribution, reserve factors and the structural mass for every sizing iteration.
FEM Input for the analytical buckling criterionThe analytical buckling criterion requires the geometry and stresses of the rectangular buckling fields as input values (formulas 6, 8, 10). The geometry is defined by the width a, the height b and the thickness t of the buckling fields. These parameters are calculated by the structural sizer at the beginning of the sizing run and are based on the FEM model of the structure. As the buckling fields have to be rectangular by definition, polygons other than rectangular and badly deformed rectangular buckling fields are excluded from the sizing process. The stress values σx, σy and τxy are calculated from the stress values of the FEM elements in this buckling field. As an example, the critical stress in x-direction σx is the mean element stress in x-direction of all FEM elements in a buckling field.
FEM Input for the FEM-based buckling criterionThe only input required for the FEM buckling criterion are one ore more solu-tions to the buckling eigenproblem. These solutions sets include the eigen-values λk and the eigenvectors vk in the form of displacement vectors for all nodes of the FEM model.
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9 Application and results
9.1 Test case «VTP rudder»
9.1.1 Simulation modelIn order to compare the new FEM-based buckling criterion with the old analyti-cal buckling criterion, it has to be tested. The test subject is a vertical tail plane (VTP) rudder of a Pilatus PC-7 aircraft as seen in Fig. 54. The rudder is an aero-dynamic control surface that allows the aircraft to be controlled around the yaw axis. The rudder is a classical aluminum aerostructure as shown in Fig. 55. It in-cludes ribs, spars and skins that are joined by rivets. While the skins are stressed by bending and torsion loads, the spars are mainly stressed by shear loads.
The ribs have two functions: Firstly, they support the aerodynamic shape of the rudder and secondly, they are required for the load introduction at the upper and lower hinge points. Ribs in real aircraft structures are sometimes further lightened by cut outs. This feature is omitted from the simulation model to
RudderVertical tail plane (VTP)
Rear fuselage
Horizontal tail plane (HTP)
Figure 54: Aircraft tail with vertical tail plane rudder
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8 Sizing criteria for thickness sizing
keep the model complexity within reasonable limits. Both the upper and lower hinges are rose joints and only transmit translational loads. The rudder mo-ment along the hinge axis is introduced at the nose rib near the lower hinge.
9.1.2 FEM modelBoth the FEM-based stress and buckling criteria require an FEM model of the rudder. As described in section 8.3.3, MSC Nastran is used for the structural analysis. The thin-walled structure is made of linear shell elements. In total, 5894 quadrilateral and triangular shell elements are used for the FEM model of the rudder structure. As the author had access to a test set-up of the real rudder structure, the quality of the FEM model was assessed with a validation study and can be descirbed as good.
xz
y
1650
mm
Upper hinge
Nose ribs
Hingeaxis
Lowerhinge
Front spar
Rear spar
Ribs
Skin
Figure 55: Rudder structure (skin and inner structure)
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9.1.3 LoadcaseThe predominant loadcase for the dimensioning of the rudder structure in-cludes aerodynamic loads due to maximum rudder deflection at high speeds. These loads act normally on both rudder side surfaces and induce bending and torsion of the rudder structure. In the FEM model, these aerodynamic loads are represented by condensed force vectors. These force vectors are applied to virtual load introduction points given by the intersection of the load axis and the rib surfaces. The actual load transfer from the load introduction points to the rib boundary curves is achieved with RBE3 interpolation elements. The boundary conditions are set as follows: The lower hinge transmits translational DOFs in all directions and one rotational DOF in direction of the hinge axis (z direction) to simulate the rudder moment. The upper hinge only transmits translational DOFs in x and y directions but not in direction of the hinge axis.
xz
y
zy
Forcevectors
Upper ball bearing
Lowerball bearing
Load axis
Hingeaxis
Figure 56: Aerodynamic loads
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9 Application and results
9.1.4 Optimization problemThe goal of the optimization is to minimize the structural weight of the rudder while achieving a target eigenvalue λtarget (buckling factor) of 1.0 or higher. Design for strength is not an issue, because the maximum stress allowables are not met even with all zone thicknesses set to the minimum allowable thick-ness. The design parameters of the optimization are as follows: The structure is split into 76 sizing zones. The thickness of each zone can be varied between a minimum thickness tmin of 0.3mm and a maximum thickness tmax of 3.0mm. The initial thickness values of the unsized ribs, spars and skins are shown in Tab. 12. There is only one static loadcase as described in subsection 9.1.3.
Table 12: Initial sizing zone properties (unsized structure)Outer skin Ribs and spars
Sizing zones
Figure 57: Sizing zones
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9.2 Results
9.2.1 Unsized structure (baseline)The unsized structure satisfies the buckling criteria with a first eigenvalue λ (buckling factor) of 1.0. The first eigenmode is shown in Fig. 58. It can be seen that the combination of compression and shear loads lead to buckling in the middle section of the right skin surface. The total mass of the structure is 4.079kg.
9.2.2 Structural sizing with analytical buckling criterionThe analytical buckling criterion is able to handle combined compression and shear buckling of simply supported rectangular plates (Appendix D). After 10 iterations the thickness distribution is fully converged and the stopping criteria
xz
y
Nod
al d
ispl
acem
ent [
-]1.0
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Figure 58: First buckling mode (unsized structure)
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9 Application and results
are met (Fig. 59). The final thickness distribution can be seen in Fig. 62. As described in section 8.3.3, the buckling fields have to be approximately rect-angular for the analytical buckling criterion to be applied. Triangular buckling fields like the nose ribs or highly curved buckling fields in the nose skin section are thus excluded from the thickness sizing and their thickness is set to the minimum allowable value tmin. The buckling fields that fulfill the geometric requirements are sized and their thickness is adjusted to a value that results in an optimal reserve factor FR against buckling. According to the analyti-cal buckling methods described in section 8.2, the sized structure fulfills the buckling criteria for compression, shear and combined compression and shear buckling. However, an FEM eigenvalue buckling analysis has been performed to verify the results. In contrary to the results of the analytical buckling method, the FEM buckling analysis shows that the structure is buckling with an eigen-value λ (buckling factor) of 0.35 (Fig. 63). First buckling occurs in the first rib from the bottom near the front spar. The trapezoidal shape of this rib and the stress concentration near the front spar lead to an overestimation of the local
Part III: FEM-based buckling criterion for structural sizing
buckling reserve factor and consequently to a buckling field thickness which is too low. The total mass of the sized structure is 3.337kg which equals a reduction of 18% compared to the mass of the unsized structure.
9.2.3 Structural sizing with FEM buckling criterionThe results of the structural sizing with the FEM-based buckling criterion are shown in Fig. 64. It can bee seen that the thickness of the buckling fields on both sides of the rudder has been increased to prevent buckling. The buckling fields with the maximum sheet thickness can be found in the middle of the right skin and near the upper and lower bearings on the left skin of the rudder. A look at the first buckling mode reveals widespread buckling throughout the structure. A first eigenvalue λ (buckling factor) of 1.01 shows that the buckling criterion is fulfilled (Fig. 65). The total mass of the sized structure is 2.592kg which equals weight savings of 36% compared to the mass of the unsized structure. After a total number of 14 iterations, the thickness distribution con-verges and the stopping criteria are met (Fig. 60).
1.51 2 6
Iteration step12 14
2.0
2.5
3.0
4.5
3 4 5 8 10
3.5
4.0
1.0
2.0
3.0
5.0
4.0
11 137 9
Mass [kg]
Max. displacement [mm]
Figure 60: Convergence (FEM buckling criterion)
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9 Application and results
9.2.4 Structural optimization with Genetic AlgorithmsIn order to evaluate the optimality of the results obtained by the structural sizer, a global optimization based on Genetic Algorithms (GAs) has been per-formed. GAs are adaptive heuristic search algorithms that are well suited for the optimization of noisy or non-convex optimization problems. The funda-mental concept of GAs is based on the principles of evolution. This includes the selection, variation and recombination of individuals populating the solu-tion space. An extensive introduction to GAs is given by Koenig [61]. Global optimization methods require the optimization problem to be formulated as a minimization problem. In this case, a global objective function O is defined as the sum of the fitness functions Fitmass for the mass and Fitbuckling for the buckling factor:
(26)Ototal = Fitmass + Fitbuckling
(27)Fitmass =
m
mtarget− 1 · 1
100 , f or m > mtarget
0 , f or m ≤ mtarget
(28)Fitbuckling =
fb − fb,target
2, f or fb < fb,target
0 , f or fb ≥ fb,target
Structures with a lower mass m and a buckling factor fb close to or above the target buckling factor fb,target thus result in lower objective function values. Generally speaking, the lower the objective function value, the better the solu-tion. Function plots of the two fitness functions for the mass and the buckling factor can bee seen in Fig. 61. Because of the stochastic nature of GAs, several optimization runs have been performed. The best solution found satisfies the FEM buckling criteria with a buckling factor of 1.0 and has a structural mass of 2.606kg. This means that the mass is higher but within 1% of the solution found with the FEM-based buckling criterion. Interestingly, the optimal thick-ness distribution found with the GA is similar but not identical to the thickness distribution found with the sizer and the FEM-based buckling criterion. In con-trary to the solution described in subsection 9.2.3, the GA tends to increase the thickness of some nose skin panels to stiffen the adjacent skin panels on either sides of the rudder. As a result, the side skin panels can be made thin-
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ner without showing buckling behavior. All in all, this leads to a best solution roughly equivalent to the one found by the sizer and the FEM-based buckling criterion in terms of structural mass and global buckling factor (Figs. 66, 67).
9.2.5 Comparison of the results
Structural efficiencyThe goal of the optimization was to minimize the structural mass while achiev-ing a first eigenvalue (buckling factor) of 1.0 or more. Tab. 13 shows an over-view of the masses and eigenvalues of the unsized and optimized structures. It can be seen, that all optimization methods resulted in a structure lighter than the unsized structure. To assess the buckling performance, an FEM eigenvalue buckling analysis has been performed for all solutions. A glance at the first eigenvalue shows that both the solutions of the structural sizing and the global optimization with GAs have a first eigenvalue of 1.0 or higher and achieve the goal of the optimization. In contrary, the solution found with the sizer using the analytical buckling criteria resulted in a critical FEM eigenvalue of 0.35, which means that the structure is buckling.
Table 13: Mass and FEM eigenvalues for all configurations
Computational efficiencyBesides the quality of the results, the computational efficiency of the different optimization methods has been measured and listed in Tab. 14. The structural sizing with the analytical buckling criterion is the computationally least expen-sive followed closely by the structural sizing with the FEM buckling criterion. The latter requires an FEM buckling analysis for every iteration which is com-putationally more expensive than the analytical buckling analysis. The global optimization performed with the GAs was the computationally least efficient
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9 Application and results
of all three methods with 25’000 FEM buckling analyses in total. It has to be noted that optimization with GAs lends itself to parallelization and 10 worksta-tions have been used in parallel to perform this optimization. Expressed in wall clock time, a single optimization run with GAs took approximately 100 times longer than the optimization with the structural sizer.
The computational efficiency of every optimization method is of course strong-ly dependent of the optimization problem (e.g. the number of buckling fields or the number of DOFs of the FEM model).
Table 14: Computational efficiency of different optimization methods
9.3 Summary
The third part of the thesis introduces a novel FEM-based buckling criterion for the thickness optimization of shell structures typically found in aerospace applications. At first, an introduction to FEM-based structural sizing, as used in the mass estimation process described in Part I, is given. Subsequently, an exemplary analytical buckling criterion for rectangular plates is introduced and the need for a higher fidelity buckling criterion based on FEM buckling analysis is shown. A review of the new FEM-based buckling criterion is given and the implementation into the existing structural sizing framework is shown.
Part III concludes with a case study: Both the analytical and the newly devel-oped FEM-based buckling criteria are used for the buckling optimization of an aircraft rudder structure. An independent third set of results is obtained through the use of global optimization with Genetic Algorithms. The com-parison of the results shows, that the FEM-based buckling criterion is indeed a viable alternative to the existing analytical buckling criteria.
In case of the optimization problem described above, the FEM-based buckling criterion offers significantly better results at the expense of a marginally higher computational cost.
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Part III: FEM-based buckling criterion for structural sizing
00 0.5
Buckling factor [-]
Buc
klin
g fit
ness
Mas
s fitn
ess
1 1.5
0.25
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1
02 3
Total mass [kg]4 5
0.005
0.01
0.015
Buc
klin
g
No
buck
ling
f b,target
mtarget
Figure 61: Fitness functions used for global optimization
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9 Application and results
Right skinLeft skin Ribs and spars
xz
y
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yx
zy
Thic
knes
s [m
m]
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ispl
acem
ent [
-]1.0
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y
xz
yx
zy
λ = 0.35
Local buckling
Figure 62: Sheet thickness (sized with analytical buckling criterion)
Figure 63: First buckling mode (sized with analytical buckling criterion)
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Part III: FEM-based buckling criterion for structural sizing
Right skinLeft skin Ribs and spars
Thic
knes
s [m
m]
1.0
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y
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acem
ent [
-]
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y
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yx
zy
λ = 1.01
Figure 64: Sheet thickness (sized with FEM buckling criterion)
Figure 65: First buckling mode (sized with FEM buckling criterion)
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9 Application and results
Right skinLeft skin Ribs and spars
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y
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yx
zy
Thic
knes
s [m
m]
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λ = 1.00
Figure 66: Sheet thickness (optimized with Genetic Algorithms)
Figure 67: First buckling mode (optimized with Genetic Algorithms)
During the preliminary design phase, fast and accurate mass estimation is es-sential for the identification and optimization of structurally efficient aircraft designs.
In contrary to the state of the art, the present work demonstrates the feasibil-ity of a mass estimation process that relies on modern CAD/CAE tools instead of custom in-house tools for the generation and handling of the computa-tional models. This offers several advantages: Firstly, a reduction in develop-ment time and cost due to the use of built-in features for the generation of the geometrical and structural models. Secondly, simplified generation of the structural model enabled by the tight integration of both CAD and CAE capabilities in one software package. Thirdly, easier data exchange between different working groups and software process by using standardized software tools and data formats. The last point is especially important as aircraft design is a multidisciplinary process that requires a high degree of collaboration be-tween teams of different disciplines such as flight physics, aerodynamics and structural mechanics.
In the first part of the thesis, the CAD/CAE-based multidisciplinary mass estima-tion process is introduced and the specific implications of using the commercial CAD/CAE software CATIA V5 as a multi-model generator are described. It is subsequently shown that CATIA V5 can not only be used for the generation of the geometrical and structural models, but also for the generation of the com-putational models used for the load calculation. A good example for this versa-tility is given by the custom CAD/CFD gateway that was implemented in CATIA V5: The external CFD code BLWF used for the calculation of the aerodynamic loads requires input files in a proprietary file format. Based on the high-quality geometrical model of the wing, the gateway allows the automatic generation of CFD input files from within the CAD environment in CATIA V5.
106
10 Conclusions and outlook
Measured in lines of code, half of the total functionality of the multidisciplinary process can be covered by CATIA V5. The rest of the functionality is covered by custom MATLAB scripts. The latter handle the processing of the aerodynamic and fuel loads, the iterative dimensioning routine (structural sizing) as well as the numerical and graphical postprocessing functionality.
However, there are several disadvantages that severely limit the practicability of the CAD/CAE-based approach pursued in this thesis. Obvious disadvantages are the fixed and recurring license costs when using commercial CAD/CAE software tools such as CATIA V5 or the dependency on fixed software update cycles. But the most import disadvantage concerns the computational effi-ciency: Within the Knowledgeware environment, CATIA V5 offers a variety of automation tools and scripting languages. The author used a combination of VBScripts, Knowledge Patterns and User Defined Features (UDFs) to automate the generation and handling of the computational models. Part I of the thesis concludes with an exemplary mass estimation of a long range aircraft wingbox structure. An analysis of the computational cost reveals that the automated generation of the geometrical, structural and aerodynamic models with CATIA V5 consumes more than one hour of computing time. An additional half an hour is used for the load application within CATIA V5. The actual time depends of course on the chosen fidelity of the computational models. Nevertheless, the computational efficiency of the automation tools in CATIA V5 is surpris-ingly low and renders multidisciplinary optimization (especially in combination with topology optimization) virtually impossible at this time. A considerable increase in computational efficiency in the order of a magnitude remains a definite requirement regarding the future use of CATIA V5 in multidisciplinary optimization.
A second disadvantage concerns the sparse documentation of the automation tools in CATIA V5. The degree of automation that can be achieved with CATIA V5 is considerable and is increased with every new version released. It is hard to understand, why this unique strategic advantage of CATIA V5 over competing CAD/CAE software is diminished by the inadequate documentation. Powerful automation tools such as VBScripts, Knowledge Patterns, UDFs and CAA C++ require good documentation in oder to allow developers in industry and sci-ence to explore their full potential.
107
10 Conclusions and outlook
The third disadvantage that became apparent during the development of the multidisciplinary process is the lack of an external programming interface in CATIA V5: Provisions for dynamic real-time control of CATIA V5 from the outside, as required for process control and error handling, are not available. A dedicated API (Application Programming Interface), e.g. based on the pro-gramming language Python, would greatly enhance the suitability of CATIA V5 for multidisciplinary processes.
Last but not least, the use of composite materials, such as CFRPs, is not pos-sible in the current version of the CAD/CAE-based mass estimation process. This is due to the fact that the automated generation of the corresponding FEM materials and element properties within the structural model is not sup-ported in the current release of CATIA V5 (R19). In consideration of the wide-spread use of composite materials in the aircraft industry, the addition of this functionality would be most welcome.
10.2 Investigation of local load introduction methods
Engineers involved in preliminary aircraft design are required to make a con-stant trade-off between model fidelity and computational efficiency. This is especially true for the fidelity of the structural model and the load introduction methods used.
The second part of the thesis uses the newly-developed CAD/CAE-based mass estimation process to investigate two load introduction methods of different fidelity (SMT loads vs. nodal loads) and their impact on the final mass distribu-tion of the wingbox structure. In comparison to low-fidelity SMT load introduc-tion, the use of high-fidelity nodal load introduction for all wing loads results in a small but significant increase in structural mass of 4%.
Subsequent analyses by load type reveal two surprising results: Firstly, aerody-namic loads, which are the most important load type by magnitude, do not benefit from the use of nodal load introduction and appear to be accurately represented by SMT loads. This is an important finding as the use of nodal loads for the modeling of aerodynamic loads is complex, labor-intensive and requires CFD tools that are able to deliver surface distributed pressure loads. Secondly, in combination with the horizontal crash loadcase, the use of nodal loads for the modeling of fuel loads has a significant impact on the structural mass of the front spar and the upper and lower wing skins. This effect can
108
not be replicated with SMT fuel loads. As expected, the use of nodal loads for landing gear and engine loads results in an increase in sheet thickness near the load introduction points and thus an increase in structural mass. It should be noted however, that the quality of the mass estimation results is influenced by the fidelity of the geometrical and structural models, the selection of load- cases and the selection of sizing criteria and are in a strict sense only valid for the case study shown in part II of the thesis.
With regard to the modeling of aerodynamic loads, the following fields of improvement remain open for further research: The potential impact of aero-dynamic loads generated by extended high-lift devices on the structural mass were not assessed in this publication. This is due to the fact that the CFD tool used for the calculation of the aerodynamic loads only supports clean aircraft configurations with fully retracted high-lift devices (flaps and slats). Although the overall aerodynamic lift forces experienced during take-off and landing are lower than during high-g maneuvers, lift forces generated by high-lift devices are known to induce high local stress concentrations in the wingbox structure and therefore impact the structural mass.
10.3 FEM-based buckling criterion for structural sizing
In the third part of the thesis, a novel FEM-based buckling criterion is intro-duced. Although not directly CAD/CAE-related, it nevertheless represents an innovative attempt to increase the accuracy of structural sizing routine with regard to buckling optimization and therefore the accuracy of the entire mass estimation process.
In case of the vertical tail plane optimization problem described in part III, the FEM-based buckling criterion offers significantly better results than the analyti-cal buckling criterion at a marginally higher computational cost. A cross-check with the results obtained with Genetic Algorithms suggest that the solution found with the FEM-based buckling criterion is indeed very close to the global optimum. The new buckling criterion was also successfully used for the struc-tural optimization of the long range aircraft wingbox structure introduced in part I of the thesis. This demonstrates that the new FEM-based buckling crite-ria can also be used for the optimization of structures with a high number of buckling fields (~103) and in combination with multiple loadcases.
10 Conclusions and outlook
109
Future enhancements should aim to increase both the accuracy and the ver-satility of the FEM-based buckling criterion. The accuracy of the FEM buckling analysis could be increased by substituting the eigenvalue buckling analysis with a more accurate, but also computationally more expensive, nonlinear buckling analysis. Even the optimization of the post-buckling behavior would be conceivable with the right buckling analysis method available.
Regarding materials, the current implementation of the structural sizer is lim-ited to isotropic material properties. Given the widespread use of compos-ite materials for lightweight structures, the ability to process materials with orthotropic characteristics would broaden the field of application. Another welcome enhancement would be the ability to optimize stringer-stiffened shell structures with respect to buckling of both the shells and the stringers as the current implementation of the FEM-based buckling criterion is limited to the buckling optimization of non-stiffened shell structures only.
10.4 Outlook
Application in multidisciplinary optimizationThe prospects regarding the application of the CAD/CAE-based mass esti-mation process in multidisciplinary optimization have already been outlined in the preceding paragraphs. Due to the large number of design variables involved in multidisciplinary optimization, a significant increase in computa-tional efficiency of the CAD/CAE-based mass estimation process is essential in order to keep the total computational cost associated with multidisciplinary optimization within acceptable limits. First and foremost, this requires gains in computational efficiency of the automation capabilities in CATIA V5. Beyond that, the remaining process functionalities outside the CAD/CAE environment need to be streamlined and optimized too: This includes the loads generation and processing as well as the iterative structural sizing routine.
By experience, a switch from the programming language MATLAB to C++ is expected to result in a significant gain in computational efficiency in the order of a magnitude. Beyond that, loadcase-wise parallelization of computational tasks in combination with distributed computing could generate further sig-nificant time savings.
10 Conclusions and outlook
110
Seamless multi-fidelity modelingUnfortunately, high fidelity of the computational models and high computa-tional efficiency can rarely be had at the same time. The problem is that the former is required for detailed analysis and the latter is required for (multidis-ciplinary) optimization. Wouldn’t it be nice, if one and the same geometrical model and its associated computational models (the structural model, the aerodynamic model, etc.) could be varied seamlessly from low-fidelity to high-fidelity? This is of course nothing new - so called multi-fidelity models have long been discussed. However, a convincing technical implementation of this concept, able to handle the model complexity shown in this thesis, has yet to be found. In this regard, it would be worthwhile to investigate the possibilities offered by CAD/CAD solutions such as CATIA V5.
10.5 Concluding remarks
Competition in the aircraft industry is tough and the established airframers in Europe and the United States are under increasing pressure from competitors in Brazil, Russia and most recently China. However, engineering excellence is as important as low production costs and demand for efficient aircraft is stronger than ever. Due to the complexity and inherently multidisciplinary na-ture of aircraft design, computational tools and processes for the analysis and optimization of aircraft designs are expected to gain even more importance in the future keeping engineers and scientists in both academia and industry busy for years to come.
Integral fuel tanks in the wingbox structure provide for most of the fuel ca-pacity in modern transport aircraft (Fig. 69). As explained in section 5.4.2, the inertial fuel loads experienced during flight maneuvers counteract the aerody-namic lift forces and lead to a reduction of the total wing bending moment. The magnitude of this load relief effect depends on the layout of the fuel tanks and the fuel distribution. The fuelling and defuelling sequences describe the order in which the individual fuel tanks are filled or emptied. Three different defuelling sequences are supported by the multidisciplinary mass estimation process: The default defuelling sequence is «equal», where the fuel is distrib-uted equally across all fuel tanks (equal fill ratio). The alternative defuelling sequences are «in-to-out», where the inner fuel tanks are emptied first, and «out-to-in» where the outer fuel tanks are emptied first. Although the total fuel mass is independent of the defuelling sequence, the spanwise location of the center of gravity of the fuel and hence the wing bending moment gener-ated by the fuel loads can vary significantly. In theory, the optimal load relief effect is achieved with the defuelling sequence «in-to-out» because it offers the biggest reduction of the wing bending moment.
B.2 Impact of the defuelling sequence on structural weight
In order to assess the qualitative and quantitative impact of the defuelling sequence on the structural weight of the wingbox, a comparative study was performed. The same aircraft configuration, material allowables, loadcases and sizing criteria as described in section 6.1 were used. Nodal load introduc-tion was used for all load types including fuel loads. The only parameter that was varied was the defuelling sequence. Tab. 15 shows the key results of the study including the maximum wing bending moment for the 2.5g maneuver
114
Appendix
Outboard engine
Slats
Ailerons
Front spar
Flaps
Landing gearCenter wingbox Mid spar
Spoilers
Rear spar
Fuel tank layoutDefueling sequences:in-to-out (1-2-3-4), out-to-in (4-3-2-1),
equal
Ribs
Inboard engine
1 (center)
2 (in
boar
d)3
(out
boar
d)
4 (ti
p)
xy
z
Figure 69: Wing and fuel tank layout
115
loadcase (#4) and the total mass of the sized wingbox structure. As expect-ed, the defuelling sequence «in-to-out» results in the lowest maximum wing bending moment and consequently the lowest structural mass. The defuelling sequence «equal», which was used as the default setting for the genera-tion of the results in Parts I & II of this publication, results in a slightly higher maximum wing bending moments and structural mass. However, the use of the defuelling sequence «out-to-in» results in a significantly higher maximum wing bending moment and structural mass.
Defuelling seq. Mb,max [Nm] ΔMb [%] Mass [kg] ΔMass [%]
Table 15: Wing root bending moment vs. wingbox mass
A graphical representation of the SMT cut loads for the 2.5g maneuver load-case (#4) is shown in Fig. 70. The total spread in maximum wing bending mo-ment amounts to approximately 10% and has a direct impact on the structural weight of the wingbox. Fig. 71 shows the resulting sized sheet thickness for the different defuelling sequences. The difference in sheet thickness in the upper and lower wing skins of the wingbox is clearly visible (Tab. 16).
Table 16: Wingbox weight breakdown for different defuelling sequences
B Defuelling sequence
116
Appendix
out-to-inequalin-to-out
Defuelling sequence
out-to-inequalin-to-out
Defuelling sequence
Spread: ~10%
out-to-inequalin-to-out
Defuelling sequence
-2e6
-1e6
0
0eta [-]
Shea
r for
ce (S
) [N
]
0.2 0.4 0.6 0.8 1
0eta [-]
0.2 0.4 0.6 0.8 1-3e6
0eta [-]
0.2 0.4 0.6 0.8 1
-2e6
-1e6
0
Ben
ding
mom
ent (
M) [
Nm
]
-6e5
-2e5
-4e5
2e5
0
Tors
ion
mom
ent (
T) [N
m]
Figure 70: SMT cut loads for different defuelling sequences (LC #4, 2.5g)
117
B Defuelling sequence
Sheet thickness [mm]
2 302010 155 25
Defuelling:in-to-out
Defuelling:equal
Defuelling:out-to-in
Figure 71: Sized thickness for different defuelling sequences
119
C Fatigue
Appendix
C Fatigue
C.1 Introduction
Fatigue plays an important role in aircraft design, especially in combination with metallic materials: Cyclic tension loads can lead to the formation of mi-croscopic cracks that – under the right circumstances – can grow and lead to structural failure long before the theoretical strength limits of the material are reached. In case of the wingbox structure, the lower wing skins are especially prone to fatigue as they are mainly stressed by (cyclic) tension loads during cruise flight.
The results of the wingbox mass estimation case study in part 1 of this thesis (Tab. 3) were obtained with the use of both stress and buckling criteria but without the use of a fatigue criterion. As a result, the upper wing skins are sig-nificantly heavier than the lower wing skins (10’793 kg vs. 6’870 kg). In reality, which means under consideration of fatigue, the opposite is usually true and the lower wing skins are slightly heavier than the upper wing skins.
C.2 Impact of fatigue on structural mass
In order to assess the specific impact of fatigue stress criteria on the structural mass of the wingbox, a numerical study was performed. The material allow-ables and the loadcases used for this study are based on the ones presented in part I of this thesis (Tabs. 1 and 2). The only difference concernes the fatigue loadcase (#7, «Cruise»), where a load factor of 1.3g was used instead of 1.0g in order to account for gust loads during cruise flight.
As the lower wing skins are made of Aluminium 2024-T351, appropriate criti-cal stress levels for the dimensioning against fatigue had to be defined. Two different fatigue stress allowables were used: A critical fatigue stress value of 138 N/mm2, which is given by the material manufacturer, and a reduced
120
critical stress value of 100 N/mm2. The reduced value accounts for imperfec-tions in the structure, such as manholes or rivets, and can be regarded as a typical and reasonable value used by aircraft manufacturers during aircraft pre-design. The study was performed with both available buckling criteria: the newly-developed FEM-based buckling criterion and the traditional analytical buckling criterion.
Results and consequencesTab. 17 shows the mass estimation results without the use a fatigue criterion. As in part 1 of this thesis, the mass of the upper wing skins exceeds the mass of the lower wing skins due to the increased sheet thickness in order to prevent buckling. As expected, the use of the fatigue criterion increases the mass of the lower wing skin while the mass of the upper wing skins remains almost constant (Tabs. 18-19). However, even with the lower fatigue stress allowable of 100 N/mm2, the mass of the lower wing skins remains significantly lower than the mass of the upper wing skins. This is due to the fact that the FEM-based buckling criterion leads to an overdimensioning of the upper wing skins as described in section 4.2.2 of this thesis.
The same study was also performed with the analytical buckling criterion (Tabs. 20-22). In contrary to the results obtained with the FEM-based buckling cri-terion, the resulting mass distribution is more realistic: Without consideration of fatigue (Tab. 20), the mass of the upper wing skins is 25% higher than the mass of the lower wing skins. When dimensioning against fatigue is consid-ered, the mass of the lower wing skins increases depending on the fatigue stress allowable used. In case of the allowable of 100 N/mm2 (Tab. 22), the mass of the lower wing skins increases and exceeds the mass of the upper wing skins by 8%.
In accordance to Tab. 22, Fig. 72 shows the sheet thickness obtained under consideration of fatigue using a fatigue stress allowable of 100 N/mm2. The isolated effect of the fatigue criterion on the sheet thickness (the difference of the sheet thicknesses obtained with and without fatigue criterion) is shown in Fig. 73. As previously stated, the increase in sheet thickness caused by the fatigue criterion is limited to the lower wing skins which are subject to tension loads during the cruise loadcase. Nevertheless, the increase in sheet thickness in the lower wing skins is considerable and justifies the complementary use of a fatigue criterion if a buckling criterion is used.
While stress criteria offer a straightforward way to achieve a fully stressed design, shell structures under compression and shear loads can be prone to buckling. Special buckling criteria allow for the calculation of buckling reserve factors that can be used for the sizing of the shell thickness. Traditionally, these reserve factors are calculated with analytical buckling methods [62]. The HSS Handbook of Structural Stability [63] describes a variety of analytical buckling models for plates of different shapes, with different supports and loads. Two analytical methods for the buckling analysis of simply supported rectangular plates under compression and shear load are described below.
D.1 Compression buckling of a simply supported plateFig. 72 shows a simply supported rectangular plate under uniaxial compression loading σx. The load is introduced at the two shorter edges of the plate. Pa-rameters a and b denote the length of the edges, t denotes the plate thickness, ν and E denote the Poisson Ratio and the Young’s Modulus of the isotropic material. According to HSS the critical buckling stress σx,crit and the reserve factor FR,cx can be calculated with the following equations:
(6)σx,crit = kc,x · π2E12(1 − ν2)
tb
2
(7)FR,cx =σx,crit
σx,init
The reference stress σx,init is the actual compression stress in the buckling field in x-direction. The buckling coefficient kc,x is provided by the graph in Fig. 74. It is worthwhile to note that kc,x does not fall off continuously with an increasing aspect ratio β but also depends on the buckling mode order m. The buckling coefficients for simply supported plates are lower than those for partially or fully clamped rectangular plates. If the exact boundary conditions at the edges
126
Appendix
30 1 2
β = a/b
kc,x
3 4
4
5
6
7
a
b
m = 1
m = 1
m = 2 m = 3
xy
0
5
10
15
20
25
30
0 1 2β = a/b
kc,xy
3 4
a
b
Figure 74: kc,x and kc,xy values for a simply supported rectangular plate
127
D Analytical buckling criterioa
of the plate are unknown, it is common practice to regard the plate as sim-ply supported, as this results in conservative estimates of the critical buckling loads. Accordingly, compression loads acting on the two shorter edges of the plate lead to the following equations for the critical buckling stress σy,crit and the reserve factor FR,cy:
(8)σy,crit = kc,y · π 2E12(1 − ν2)
ta
2
(9)FR,cy =σy,crit
σy,init
D.2 Shear buckling of a simply supported plateA simply supported rectangular plate under uniform shear load can be seen in the lower half of Fig. 74. In analogy to compression buckling, the critical buckling shear stress τxy,crit and reserve factor FR,sxy are given by:
(10)τxy,crit = kc,xy · π2E12(1 − ν2)
tb
2
(11)FR,sxy =τxy,crit
τxy,init
D.3 Combined compression and shear bucklingIn some cases, compression and shear loads act on the buckling field simul-taneously. This can lead to even lower values of the buckling reserve factors. According to HSS [63] and Bruhn [41] the total buckling reserve factor FR,tot for combined compression and shear loads can be calculated as follows:
(12)1
FR,tot=
1FR,cx
+1
FR,cy+
1FR,sxy
2
D.4 Calculation of the sized buckling field thicknessAs seen in the formulas for compression and shear buckling, the critical stress is roughly proportional to the square of the buckling field thickness. In case of compression buckling, the total compression load Fx is:
128
Appendix
(13)Fx = σx · tb
This leads us to the following relation between the reserve factor FR and the buckling field thickness t:
(14)FR ∝ t3
With the total buckling reserve factor now known, the sized buckling field thickness can be calculated as follows:
(15)tsized = tinit · 3 FS
FR,tot
129
D Analytical buckling criterioa
131
List of Figures
List of Figures
1 Airbus milestones model (early stages) 3
2 Costs during aircraft development 3
3 Characteristics of a basic mass estimation process 5
4 FAME-W design process [15] 7
5 FAME-W geometrical model (wireframe) [17] 8
6 FAME-W structural model [17] 8
7 PrADO geometrical model (Airbus A320) [8] 10
8 PrADO structural model (Airbus A320) [8] 10
9 MDCAD Framework [24] 11
10 Qualitative comparison of existing mass estimation tools 12
11 Aircraft geometry model by Ledermann [29] 13
12 Research needs 15
13 DLR-F11 wing planform 19
14 Multidisciplinary process 20
15 CATIA V5 automation tiers 22
16 Implemented automation concept 23
17 Parametric-associative CAD model of an aircraft wing 24
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* Submitted for publication, June 2010. Preprints available from: ETH Zurich, Centre of Structure Technologies, Leonhardstrasse 27, CH-8092 Zurich, www.structures.ethz.ch
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Own publications
Own publications
[1] F. Hürlimann, R. Kelm, M. Dugas, K. Oltmann, G. Kress, Mass estimation of transport aircraft wingbox structures with a CAD/CAE-based multidisciplinary process, Centre of Structure Technologies, ETH Zurich, Aerospace Science & Technology (Elsevier), accepted for publication, July 2010
[2] F. Hürlimann, R. Kelm, M. Dugas, G. Kress, Investigation of local load introduction methods in aircraft pre-design, Centre of Structure Technologies, ETH Zurich, IMES-ST-10-030, 2010*
[3] F. Hürlimann, M. Pfister, G. Kress, A sizing strategy for the buckling optimization of shell structures using an FEM-based buckling criterion, Centre of Structure Technologies, ETH Zurich, IMES-ST-031, 2010*
[4] F. Hürlimann, P. Ermanni, G. Kress, Massenabschätzung von Trag-flügelstrukturen in der Flugzeugvorauslegung mit einem CAD/CAE-basierten multidisziplinären Simulationsprozess, Proceedings, DGLR Kongress 2008, Darmstadt, 2008
[5] C. Ledermann, F. Hürlimann, M. Wintermantel, P. Ermanni, Coupling library for aeroelastic simulation in aircraft pre-design, Proceedings, International Forum on Aeroelasticity and Structural Dynamics 2005, IFASD 2005. CEAS/AIAA/DGLR, ISBN 3-932182-43-X, Munich, Germany, June 28 - July 01, 2005
* Submitted for publication, June 2010. Preprints available from: ETH Zurich, Centre of Structure Technologies, Leonhardstrasse 27, CH-8092 Zurich, www.structures.ethz.ch
09/05 - 06/10 PhD studies, Centre of Structure Technologies, ETH Zurich
10/04 - 04/05 Diploma thesis, Design and development of an aeroelastic coupling library, in cooperation with Sauber Petronas F1
10/98 - 10/04 Studies in Mechanical Engineering, ETH Zurich (Dipl. Masch.-Ing. ETH), Specialization in Lightweight Structures and Aerothermochemistry & Combustion Systems
07/02 - 11/02 Military service, anti-aircraft artillery, Swiss Air Force
08/93 - 07/98 Matura (Typus C), Kantonsschule Zug
Working experience
09/05 - 06/09 IT Administrator, Centre of Structure Technologies, ETHZ
02/05 - 08/05 Assistant worker at the Aerothermochemistry and Combustion Systems Laboratory, ETHZ
04/99 - 06/99 Internship at Schweizerische Flugzeugwerke, Alpnach
Diss. ETH No 19458
Mass Estimation of Transport Aircraft Wingbox Structures with a CAD/CAE-
